Algebra Examples

$\frac{2 x + 5}{17} - (5 - y) = - 60$ $\frac{y + 62}{2} - (1 - x) = 40$

Step 1

Solve for $x$ in $\frac{2 x + 5}{17} - 5 + y = - 60$ .

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Step 1.1

Simplify $\frac{2 x + 5}{17} - 5 + y$ .

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Step 1.1.1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$\frac{2 x + 5}{17} - 5 \cdot \frac{17}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.2

Combine $- 5$ and $\frac{17}{17}$ .

$\frac{2 x + 5}{17} + \frac{- 5 \cdot 17}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.3

Combine the numerators over the common denominator.

$\frac{2 x + 5 - 5 \cdot 17}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.4

Simplify the expression.

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Step 1.1.4.1

Multiply $- 5$ by $17$ .

$\frac{2 x + 5 - 85}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.4.2

Subtract $85$ from $5$ .

$\frac{2 x - 80}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

$\frac{2 x - 80}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.5

Factor $2$ out of $2 x - 80$ .

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Step 1.1.5.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 80}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.5.2

Factor $2$ out of $- 80$ .

$\frac{2 x + 2 \cdot - 40}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.5.3

Factor $2$ out of $2 x + 2 \cdot - 40$ .

$\frac{2 (x - 40)}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

$\frac{2 (x - 40)}{17} + y = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.6

To write $y$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$\frac{2 (x - 40)}{17} + y \cdot \frac{17}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.7

Simplify terms.

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Step 1.1.7.1

Combine $y$ and $\frac{17}{17}$ .

$\frac{2 (x - 40)}{17} + \frac{y \cdot 17}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.7.2

Combine the numerators over the common denominator.

$\frac{2 (x - 40) + y \cdot 17}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

$\frac{2 (x - 40) + y \cdot 17}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.8

Simplify the numerator.

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Step 1.1.8.1

Apply the distributive property.

$\frac{2 x + 2 \cdot - 40 + y \cdot 17}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.8.2

Multiply $2$ by $- 40$ .

$\frac{2 x - 80 + y \cdot 17}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.1.8.3

Move $17$ to the left of $y$ .

$\frac{2 x - 80 + 17 y}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

$\frac{2 x - 80 + 17 y}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

$\frac{2 x - 80 + 17 y}{17} = - 60$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.2

Multiply both sides by $17$ .

$\frac{2 x - 80 + 17 y}{17} \cdot 17 = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $\frac{2 x - 80 + 17 y}{17} \cdot 17$ .

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Step 1.3.1.1.1

Cancel the common factor of $17$ .

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Step 1.3.1.1.1.1

Cancel the common factor.

$\frac{2 x - 80 + 17 y}{17} \cdot 17 = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.3.1.1.1.2

Rewrite the expression.

$2 x - 80 + 17 y = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

$2 x - 80 + 17 y = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.3.1.1.2

Move $- 80$ .

$2 x + 17 y - 80 = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

$2 x + 17 y - 80 = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

$2 x + 17 y - 80 = - 60 \cdot 17$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $- 60$ by $17$ .

$2 x + 17 y - 80 = - 1020$

$\frac{y + 62}{2} - 1 + x = 40$

$2 x + 17 y - 80 = - 1020$

$\frac{y + 62}{2} - 1 + x = 40$

$2 x + 17 y - 80 = - 1020$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4

Solve for $x$ .

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Step 1.4.1

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

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Step 1.4.1.1

Subtract $17 y$ from both sides of the equation.

$2 x - 80 = - 1020 - 17 y$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.1.2

Add $80$ to both sides of the equation.

$2 x = - 1020 - 17 y + 80$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.1.3

Add $- 1020$ and $80$ .

$2 x = - 17 y - 940$

$\frac{y + 62}{2} - 1 + x = 40$

$2 x = - 17 y - 940$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.2

Divide each term in $2 x = - 17 y - 940$ by $2$ and simplify.

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Step 1.4.2.1

Divide each term in $2 x = - 17 y - 940$ by $2$ .

$\frac{2 x}{2} = \frac{- 17 y}{2} + \frac{- 940}{2}$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Cancel the common factor of $2$ .

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Step 1.4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 17 y}{2} + \frac{- 940}{2}$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 17 y}{2} + \frac{- 940}{2}$

$\frac{y + 62}{2} - 1 + x = 40$

$x = \frac{- 17 y}{2} + \frac{- 940}{2}$

$\frac{y + 62}{2} - 1 + x = 40$

$x = \frac{- 17 y}{2} + \frac{- 940}{2}$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.2.3

Simplify the right side.

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Step 1.4.2.3.1

Simplify each term.

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Step 1.4.2.3.1.1

Move the negative in front of the fraction.

$x = - \frac{17 y}{2} + \frac{- 940}{2}$

$\frac{y + 62}{2} - 1 + x = 40$

Step 1.4.2.3.1.2

Divide $- 940$ by $2$ .

$x = - \frac{17 y}{2} - 470$

$\frac{y + 62}{2} - 1 + x = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{y + 62}{2} - 1 + x = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{y + 62}{2} - 1 + x = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{y + 62}{2} - 1 + x = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{y + 62}{2} - 1 + x = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{y + 62}{2} - 1 + x = 40$

Step 2

Replace all occurrences of $x$ with $- \frac{17 y}{2} - 470$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $\frac{y + 62}{2} - 1 + x = 40$ with $- \frac{17 y}{2} - 470$ .

$\frac{y + 62}{2} - 1 - \frac{17 y}{2} - 470 = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{y + 62}{2} - 1 - \frac{17 y}{2} - 470$ .

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Step 2.2.1.1

Remove parentheses.

$\frac{y + 62}{2} - 1 - \frac{17 y}{2} - 470 = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.2

Combine the numerators over the common denominator.

$- 1 - 470 + \frac{y + 62 - 17 y}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.3

Subtract $17 y$ from $y$ .

$- 1 - 470 + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.4

Find the common denominator.

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Step 2.2.1.4.1

Write $- 1$ as a fraction with denominator $1$ .

$\frac{- 1}{1} - 470 + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.4.2

Multiply $\frac{- 1}{1}$ by $\frac{2}{2}$ .

$\frac{- 1}{1} \cdot \frac{2}{2} - 470 + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.4.3

Multiply $\frac{- 1}{1}$ by $\frac{2}{2}$ .

$\frac{- 1 \cdot 2}{2} - 470 + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.4.4

Write $- 470$ as a fraction with denominator $1$ .

$\frac{- 1 \cdot 2}{2} + \frac{- 470}{1} + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.4.5

Multiply $\frac{- 470}{1}$ by $\frac{2}{2}$ .

$\frac{- 1 \cdot 2}{2} + \frac{- 470}{1} \cdot \frac{2}{2} + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.4.6

Multiply $\frac{- 470}{1}$ by $\frac{2}{2}$ .

$\frac{- 1 \cdot 2}{2} + \frac{- 470 \cdot 2}{2} + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{- 1 \cdot 2}{2} + \frac{- 470 \cdot 2}{2} + \frac{- 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.5

Combine the numerators over the common denominator.

$\frac{- 1 \cdot 2 - 470 \cdot 2 - 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.6

Simplify each term.

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Step 2.2.1.6.1

Multiply $- 1$ by $2$ .

$\frac{- 2 - 470 \cdot 2 - 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.6.2

Multiply $- 470$ by $2$ .

$\frac{- 2 - 940 - 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

$\frac{- 2 - 940 - 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7

Reduce the expression by cancelling the common factors.

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Step 2.2.1.7.1

Subtract $940$ from $- 2$ .

$\frac{- 942 - 16 y + 62}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.2

Add $- 942$ and $62$ .

$\frac{- 16 y - 880}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3

Cancel the common factor of $- 16 y - 880$ and $2$ .

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Step 2.2.1.7.3.1

Factor $2$ out of $- 16 y$ .

$\frac{2 (- 8 y) - 880}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3.2

Factor $2$ out of $- 880$ .

$\frac{2 (- 8 y) + 2 \cdot - 440}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3.3

Factor $2$ out of $2 (- 8 y) + 2 (- 440)$ .

$\frac{2 (- 8 y - 440)}{2} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3.4

Cancel the common factors.

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Step 2.2.1.7.3.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 8 y - 440)}{2 (1)} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3.4.2

Cancel the common factor.

$\frac{2 (- 8 y - 440)}{2 \cdot 1} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3.4.3

Rewrite the expression.

$\frac{- 8 y - 440}{1} = 40$

$x = - \frac{17 y}{2} - 470$

Step 2.2.1.7.3.4.4

Divide $- 8 y - 440$ by $1$ .

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

$- 8 y - 440 = 40$

$x = - \frac{17 y}{2} - 470$

Step 3

Solve for $y$ in $- 8 y - 440 = 40$ .

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Step 3.1

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

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Step 3.1.1

Add $440$ to both sides of the equation.

$- 8 y = 40 + 440$

$x = - \frac{17 y}{2} - 470$

Step 3.1.2

Add $40$ and $440$ .

$- 8 y = 480$

$x = - \frac{17 y}{2} - 470$

$- 8 y = 480$

$x = - \frac{17 y}{2} - 470$

Step 3.2

Divide each term in $- 8 y = 480$ by $- 8$ and simplify.

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Step 3.2.1

Divide each term in $- 8 y = 480$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{480}{- 8}$

$x = - \frac{17 y}{2} - 470$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{480}{- 8}$

$x = - \frac{17 y}{2} - 470$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{480}{- 8}$

$x = - \frac{17 y}{2} - 470$

$y = \frac{480}{- 8}$

$x = - \frac{17 y}{2} - 470$

$y = \frac{480}{- 8}$

$x = - \frac{17 y}{2} - 470$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $480$ by $- 8$ .

$y = - 60$

$x = - \frac{17 y}{2} - 470$

$y = - 60$

$x = - \frac{17 y}{2} - 470$

$y = - 60$

$x = - \frac{17 y}{2} - 470$

$y = - 60$

$x = - \frac{17 y}{2} - 470$

Step 4

Replace all occurrences of $y$ with $- 60$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - \frac{17 y}{2} - 470$ with $- 60$ .

$x = - \frac{17 (- 60)}{2} - 470$

$y = - 60$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{17 (- 60)}{2} - 470$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Cancel the common factor of $- 60$ and $2$ .

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Step 4.2.1.1.1.1

Factor $2$ out of $17 (- 60)$ .

$x = - \frac{2 (17 \cdot (- 30))}{2} - 470$

$y = - 60$

Step 4.2.1.1.1.2

Cancel the common factors.

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Step 4.2.1.1.1.2.1

Factor $2$ out of $2$ .

$x = - \frac{2 (17 \cdot (- 30))}{2 (1)} - 470$

$y = - 60$

Step 4.2.1.1.1.2.2

Cancel the common factor.

$x = - \frac{2 (17 \cdot (- 30))}{2 \cdot 1} - 470$

$y = - 60$

Step 4.2.1.1.1.2.3

Rewrite the expression.

$x = - \frac{17 \cdot (- 30)}{1} - 470$

$y = - 60$

Step 4.2.1.1.1.2.4

Divide $17 \cdot (- 30)$ by $1$ .

$x = - (17 \cdot (- 30)) - 470$

$y = - 60$

$x = - (17 \cdot (- 30)) - 470$

$y = - 60$

$x = - (17 \cdot (- 30)) - 470$

$y = - 60$

Step 4.2.1.1.2

Multiply $- (17 \cdot (- 30))$ .

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Step 4.2.1.1.2.1

Multiply $17$ by $- 30$ .

$x = 510 - 470$

$y = - 60$

Step 4.2.1.1.2.2

Multiply $- 1$ by $- 510$ .

$x = 510 - 470$

$y = - 60$

$x = 510 - 470$

$y = - 60$

$x = 510 - 470$

$y = - 60$

Step 4.2.1.2

Subtract $470$ from $510$ .

$x = 40$

$y = - 60$

$x = 40$

$y = - 60$

$x = 40$

$y = - 60$

$x = 40$

$y = - 60$

Step 5

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

$(40, - 60)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(40, - 60)$

Equation Form:

$x = 40, y = - 60$

Step 7