Algebra Examples

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$ $2 y - \frac{5 x + 4}{11} = \frac{x + 24}{2}$

Step 1

Solve for $x$ in $2 y - \frac{5 x + 4}{11} = \frac{x + 24}{2}$ .

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Step 1.1

Multiply both sides by $2$ .

$(2 y - \frac{5 x + 4}{11}) \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Simplify $(2 y - \frac{5 x + 4}{11}) \cdot 2$ .

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Step 1.2.1.1.1

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$(2 y \cdot \frac{11}{11} - \frac{5 x + 4}{11}) \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.2

Simplify terms.

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Step 1.2.1.1.2.1

Combine $2 y$ and $\frac{11}{11}$ .

$(\frac{2 y \cdot 11}{11} - \frac{5 x + 4}{11}) \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{2 y \cdot 11 - (5 x + 4)}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 y \cdot 11 - (5 x + 4)}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.3

Simplify the numerator.

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Step 1.2.1.1.3.1

Multiply $11$ by $2$ .

$\frac{22 y - (5 x + 4)}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.3.2

Apply the distributive property.

$\frac{22 y - (5 x) - 1 \cdot 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.3.3

Multiply $5$ by $- 1$ .

$\frac{22 y - 5 x - 1 \cdot 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.3.4

Multiply $- 1$ by $4$ .

$\frac{22 y - 5 x - 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{22 y - 5 x - 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.4

Combine fractions.

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Step 1.2.1.1.4.1

Combine $\frac{22 y - 5 x - 4}{11}$ and $2$ .

$\frac{(22 y - 5 x - 4) \cdot 2}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.1.1.4.2

Move $2$ to the left of $22 y - 5 x - 4$ .

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.2.2.1.2

Rewrite the expression.

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3

Solve for $x$ .

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Step 1.3.1

Multiply both sides by $11$ .

$\frac{2 (22 y - 5 x - 4)}{11} \cdot 11 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2

Simplify.

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Step 1.3.2.1

Simplify the left side.

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Step 1.3.2.1.1

Simplify $\frac{2 (22 y - 5 x - 4)}{11} \cdot 11$ .

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Step 1.3.2.1.1.1

Cancel the common factor of $11$ .

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Step 1.3.2.1.1.1.1

Cancel the common factor.

$\frac{2 (22 y - 5 x - 4)}{11} \cdot 11 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.1.1.1.2

Rewrite the expression.

$2 (22 y - 5 x - 4) = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$2 (22 y - 5 x - 4) = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.1.1.2

Apply the distributive property.

$2 (22 y) + 2 (- 5 x) + 2 \cdot - 4 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.1.1.3

Simplify.

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Step 1.3.2.1.1.3.1

Multiply $22$ by $2$ .

$44 y + 2 (- 5 x) + 2 \cdot - 4 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.1.1.3.2

Multiply $- 5$ by $2$ .

$44 y - 10 x + 2 \cdot - 4 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.1.1.3.3

Multiply $2$ by $- 4$ .

$44 y - 10 x - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$44 y - 10 x - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.1.1.4

Reorder $44 y$ and $- 10 x$ .

$- 10 x + 44 y - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.2

Simplify the right side.

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Step 1.3.2.2.1

Simplify $(x + 24) \cdot 11$ .

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Step 1.3.2.2.1.1

Apply the distributive property.

$- 10 x + 44 y - 8 = x \cdot 11 + 24 \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.2.1.2

Simplify the expression.

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Step 1.3.2.2.1.2.1

Move $11$ to the left of $x$ .

$- 10 x + 44 y - 8 = 11 \cdot x + 24 \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.2.2.1.2.2

Multiply $24$ by $11$ .

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3

Solve for $x$ .

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Step 1.3.3.1

Move all terms containing $x$ to the left side of the equation.

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Step 1.3.3.1.1

Subtract $11 x$ from both sides of the equation.

$- 10 x + 44 y - 8 - 11 x = 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.1.2

Subtract $11 x$ from $- 10 x$ .

$- 21 x + 44 y - 8 = 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 21 x + 44 y - 8 = 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 1.3.3.2.1

Subtract $44 y$ from both sides of the equation.

$- 21 x - 8 = 264 - 44 y$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.2.2

Add $8$ to both sides of the equation.

$- 21 x = 264 - 44 y + 8$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.2.3

Add $264$ and $8$ .

$- 21 x = - 44 y + 272$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 21 x = - 44 y + 272$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.3

Divide each term in $- 21 x = - 44 y + 272$ by $- 21$ and simplify.

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Step 1.3.3.3.1

Divide each term in $- 21 x = - 44 y + 272$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.3.2

Simplify the left side.

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Step 1.3.3.3.2.1

Cancel the common factor of $- 21$ .

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Step 1.3.3.3.2.1.1

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.3.3

Simplify the right side.

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Step 1.3.3.3.3.1

Simplify each term.

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Step 1.3.3.3.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{44 y}{21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 1.3.3.3.3.1.2

Move the negative in front of the fraction.

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 2

Replace all occurrences of $x$ with $\frac{44 y}{21} - \frac{272}{21}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$ with $\frac{44 y}{21} - \frac{272}{21}$ .

$(\frac{44 y}{21} - \frac{272}{21}) - \frac{3 (\frac{44 y}{21} - \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $(\frac{44 y}{21} - \frac{272}{21}) - \frac{3 (\frac{44 y}{21} - \frac{272}{21}) + 4}{7}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Simplify the numerator.

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Step 2.2.1.1.1.1

Apply the distributive property.

$\frac{44 y}{21} - \frac{272}{21} - \frac{3 (\frac{44 y}{21}) + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.1.2.1

Factor $3$ out of $21$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{3 (\frac{44 y}{3 (7)}) + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.2.2

Cancel the common factor.

$\frac{44 y}{21} - \frac{272}{21} - \frac{3 (\frac{44 y}{3 \cdot 7}) + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.2.3

Rewrite the expression.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.1.1.3.1

Move the leading negative in $- \frac{272}{21}$ into the numerator.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (\frac{- 272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.3.2

Factor $3$ out of $21$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (\frac{- 272}{3 (7)}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.3.3

Cancel the common factor.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (\frac{- 272}{3 \cdot 7}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.3.4

Rewrite the expression.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272}{7} + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272}{7} + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.4

Move the negative in front of the fraction.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} - \frac{272}{7} + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.5

To write $4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} - \frac{272}{7} + 4 \cdot \frac{7}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.6

Combine $4$ and $\frac{7}{7}$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} - \frac{272}{7} + \frac{4 \cdot 7}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.7

Combine the numerators over the common denominator.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272 + 4 \cdot 7}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.8

Simplify the numerator.

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Step 2.2.1.1.1.8.1

Multiply $4$ by $7$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272 + 28}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.8.2

Add $- 272$ and $28$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.9

Combine the numerators over the common denominator.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y - 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.10

Factor $4$ out of $44 y - 244$ .

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Step 2.2.1.1.1.10.1

Factor $4$ out of $44 y$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y) - 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.10.2

Factor $4$ out of $- 244$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y) + 4 (- 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.1.10.3

Factor $4$ out of $4 (11 y) + 4 (- 61)$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y - 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y - 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y - 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{44 y}{21} - \frac{272}{21} - (\frac{4 (11 y - 61)}{7} \cdot \frac{1}{7}) = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.3

Multiply $\frac{4 (11 y - 61)}{7} \cdot \frac{1}{7}$ .

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Step 2.2.1.1.3.1

Multiply $\frac{4 (11 y - 61)}{7}$ by $\frac{1}{7}$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{7 \cdot 7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.1.3.2

Multiply $7$ by $7$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{49} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{49} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{49} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.2

To write $\frac{44 y}{21}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{44 y}{21} \cdot \frac{7}{7} - \frac{4 (11 y - 61)}{49} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.3

To write $- \frac{4 (11 y - 61)}{49}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{44 y}{21} \cdot \frac{7}{7} - \frac{4 (11 y - 61)}{49} \cdot \frac{3}{3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.4

Write each expression with a common denominator of $147$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.4.1

Multiply $\frac{44 y}{21}$ by $\frac{7}{7}$ .

$\frac{44 y \cdot 7}{21 \cdot 7} - \frac{4 (11 y - 61)}{49} \cdot \frac{3}{3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.4.2

Multiply $21$ by $7$ .

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61)}{49} \cdot \frac{3}{3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.4.3

Multiply $\frac{4 (11 y - 61)}{49}$ by $\frac{3}{3}$ .

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61) \cdot 3}{49 \cdot 3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.4.4

Multiply $49$ by $3$ .

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.5

Combine the numerators over the common denominator.

$\frac{44 y \cdot 7 - 4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6

Simplify the numerator.

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Step 2.2.1.6.1

Factor $4$ out of $44 y \cdot 7 - 4 (11 y - 61) \cdot 3$ .

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Step 2.2.1.6.1.1

Factor $4$ out of $44 y \cdot 7$ .

$\frac{4 (11 y \cdot 7) - 4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.1.2

Factor $4$ out of $- 4 (11 y - 61) \cdot 3$ .

$\frac{4 (11 y \cdot 7) + 4 (- (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.1.3

Factor $4$ out of $4 (11 y \cdot 7) + 4 (- (11 y - 61) \cdot 3)$ .

$\frac{4 (11 y \cdot 7 - (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (11 y \cdot 7 - (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.2

Multiply $7$ by $11$ .

$\frac{4 (77 y - (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.3

Apply the distributive property.

$\frac{4 (77 y + (- (11 y) + 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.4

Multiply $11$ by $- 1$ .

$\frac{4 (77 y + (- 11 y + 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.5

Multiply $- 1$ by $- 61$ .

$\frac{4 (77 y + (- 11 y + 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.6

Apply the distributive property.

$\frac{4 (77 y - 11 y \cdot 3 + 61 \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.7

Multiply $3$ by $- 11$ .

$\frac{4 (77 y - 33 y + 61 \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.8

Multiply $61$ by $3$ .

$\frac{4 (77 y - 33 y + 183)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.6.9

Subtract $33 y$ from $77 y$ .

$\frac{4 (44 y + 183)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y + 183)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.7

To write $- \frac{272}{21}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4 (44 y + 183)}{147} - \frac{272}{21} \cdot \frac{7}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.8

Write each expression with a common denominator of $147$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.8.1

Multiply $\frac{272}{21}$ by $\frac{7}{7}$ .

$\frac{4 (44 y + 183)}{147} - \frac{272 \cdot 7}{21 \cdot 7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.8.2

Multiply $21$ by $7$ .

$\frac{4 (44 y + 183)}{147} - \frac{272 \cdot 7}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y + 183)}{147} - \frac{272 \cdot 7}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.9

Combine the numerators over the common denominator.

$\frac{4 (44 y + 183) - 272 \cdot 7}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.10

Simplify the numerator.

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Step 2.2.1.10.1

Factor $4$ out of $4 (44 y + 183) - 272 \cdot 7$ .

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Step 2.2.1.10.1.1

Factor $4$ out of $- 272 \cdot 7$ .

$\frac{4 (44 y + 183) + 4 (- 68 \cdot 7)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.10.1.2

Factor $4$ out of $4 (44 y + 183) + 4 (- 68 \cdot 7)$ .

$\frac{4 (44 y + 183 - 68 \cdot 7)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y + 183 - 68 \cdot 7)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.10.2

Multiply $- 68$ by $7$ .

$\frac{4 (44 y + 183 - 476)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 2.2.1.10.3

Subtract $476$ from $183$ .

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3

Solve for $y$ in $\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$ .

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Step 3.1

Multiply both sides by $147$ .

$\frac{4 (44 y - 293)}{147} \cdot 147 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{4 (44 y - 293)}{147} \cdot 147$ .

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Step 3.2.1.1.1

Cancel the common factor of $147$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{4 (44 y - 293)}{147} \cdot 147 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.1.1.1.2

Rewrite the expression.

$4 (44 y - 293) = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$4 (44 y - 293) = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.1.1.2

Apply the distributive property.

$4 (44 y) + 4 \cdot - 293 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $44$ by $4$ .

$176 y + 4 \cdot - 293 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.1.1.3.2

Multiply $4$ by $- 293$ .

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $\frac{y + 2}{3} \cdot 147$ .

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Step 3.2.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1.1

Factor $3$ out of $147$ .

$176 y - 1172 = \frac{y + 2}{3} \cdot (3 (49))$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.2.1.1.2

Cancel the common factor.

$176 y - 1172 = \frac{y + 2}{3} \cdot (3 \cdot 49)$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.2.1.1.3

Rewrite the expression.

$176 y - 1172 = (y + 2) \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = (y + 2) \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.2.1.2

Apply the distributive property.

$176 y - 1172 = y \cdot 49 + 2 \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.2.1.3

Simplify the expression.

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Step 3.2.2.1.3.1

Move $49$ to the left of $y$ .

$176 y - 1172 = 49 \cdot y + 2 \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.2.2.1.3.2

Multiply $2$ by $49$ .

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3

Solve for $y$ .

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Step 3.3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.3.1.1

Subtract $49 y$ from both sides of the equation.

$176 y - 1172 - 49 y = 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.1.2

Subtract $49 y$ from $176 y$ .

$127 y - 1172 = 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$127 y - 1172 = 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.2

Move all terms not containing $y$ to the right side of the equation.

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Step 3.3.2.1

Add $1172$ to both sides of the equation.

$127 y = 98 + 1172$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.2.2

Add $98$ and $1172$ .

$127 y = 1270$

$x = \frac{44 y}{21} - \frac{272}{21}$

$127 y = 1270$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.3

Divide each term in $127 y = 1270$ by $127$ and simplify.

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Step 3.3.3.1

Divide each term in $127 y = 1270$ by $127$ .

$\frac{127 y}{127} = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $127$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{127 y}{127} = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $1270$ by $127$ .

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 4

Replace all occurrences of $y$ with $10$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{44 y}{21} - \frac{272}{21}$ with $10$ .

$x = \frac{44 (10)}{21} - \frac{272}{21}$

$y = 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{44 (10)}{21} - \frac{272}{21}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{44 (10) - 272}{21}$

$y = 10$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $44$ by $10$ .

$x = \frac{440 - 272}{21}$

$y = 10$

Step 4.2.1.2.2

Subtract $272$ from $440$ .

$x = \frac{168}{21}$

$y = 10$

Step 4.2.1.2.3

Divide $168$ by $21$ .

$x = 8$

$y = 10$

$x = 8$

$y = 10$

$x = 8$

$y = 10$

$x = 8$

$y = 10$

$x = 8$

$y = 10$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(8, 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, 10)$

Equation Form:

$x = 8, y = 10$

Step 7