Algebra Examples

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

Step 1

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

$y = \frac{4 x}{7}$

$\frac{2}{3} x = y + \frac{5}{7}$

Step 2

Replace all occurrences of $y$ with $\frac{4 x}{7}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $\frac{2}{3} x = y + \frac{5}{7}$ with $\frac{4 x}{7}$ .

$\frac{2}{3} x = (\frac{4 x}{7}) + \frac{5}{7}$

$y = \frac{4 x}{7}$

Step 2.2

Simplify $\frac{2}{3} x = (\frac{4 x}{7}) + \frac{5}{7}$ .

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} = (\frac{4 x}{7}) + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = (\frac{4 x}{7}) + \frac{5}{7}$

$y = \frac{4 x}{7}$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Remove parentheses.

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

Step 3

Solve for $x$ in $\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$ .

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Step 3.1

Multiply both sides by $3$ .

$\frac{2 x}{3} \cdot 3 = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

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

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{2 x}{3} \cdot 3 = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

Step 3.2.1.1.2

Rewrite the expression.

$2 x = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

$2 x = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

$2 x = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(\frac{4 x}{7} + \frac{5}{7}) \cdot 3$ .

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Step 3.2.2.1.1

Apply the distributive property.

$2 x = \frac{4 x}{7} \cdot 3 + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

Step 3.2.2.1.2

Multiply $\frac{4 x}{7} \cdot 3$ .

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Step 3.2.2.1.2.1

Combine $\frac{4 x}{7}$ and $3$ .

$2 x = \frac{4 x \cdot 3}{7} + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

Step 3.2.2.1.2.2

Multiply $3$ by $4$ .

$2 x = \frac{12 x}{7} + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

Step 3.2.2.1.3

Multiply $\frac{5}{7} \cdot 3$ .

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Step 3.2.2.1.3.1

Combine $\frac{5}{7}$ and $3$ .

$2 x = \frac{12 x}{7} + \frac{5 \cdot 3}{7}$

$y = \frac{4 x}{7}$

Step 3.2.2.1.3.2

Multiply $5$ by $3$ .

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $\frac{12 x}{7}$ from both sides of the equation.

$2 x - \frac{12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 x \cdot \frac{7}{7} - \frac{12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.3

Combine $2 x$ and $\frac{7}{7}$ .

$\frac{2 x \cdot 7}{7} - \frac{12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 7 - 12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.5

Simplify the numerator.

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Step 3.3.1.5.1

Factor $2 x$ out of $2 x \cdot 7 - 12 x$ .

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Step 3.3.1.5.1.1

Factor $2 x$ out of $2 x \cdot 7$ .

$\frac{2 x (7) - 12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.5.1.2

Factor $2 x$ out of $- 12 x$ .

$\frac{2 x (7) + 2 x (- 6)}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.5.1.3

Factor $2 x$ out of $2 x (7) + 2 x (- 6)$ .

$\frac{2 x (7 - 6)}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x (7 - 6)}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.5.2

Subtract $6$ from $7$ .

$\frac{2 x \cdot 1}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.1.5.3

Multiply $2$ by $1$ .

$\frac{2 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Step 3.3.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2 x = 15$

$y = \frac{4 x}{7}$

Step 3.3.3

Divide each term in $2 x = 15$ by $2$ and simplify.

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Step 3.3.3.1

Divide each term in $2 x = 15$ by $2$ .

$\frac{2 x}{2} = \frac{15}{2}$

$y = \frac{4 x}{7}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{15}{2}$

$y = \frac{4 x}{7}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

Step 4

Replace all occurrences of $x$ with $\frac{15}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{4 x}{7}$ with $\frac{15}{2}$ .

$y = \frac{4 (\frac{15}{2})}{7}$

$x = \frac{15}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4 (\frac{15}{2})}{7}$ .

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Step 4.2.1.1

Combine $4$ and $\frac{15}{2}$ .

$y = \frac{\frac{4 \cdot 15}{2}}{7}$

$x = \frac{15}{2}$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $4$ by $15$ .

$y = \frac{\frac{60}{2}}{7}$

$x = \frac{15}{2}$

Step 4.2.1.2.2

Divide $60$ by $2$ .

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

Step 5

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

$(\frac{15}{2}, \frac{30}{7})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{15}{2}, \frac{30}{7})$

Equation Form:

$x = \frac{15}{2}, y = \frac{30}{7}$

Step 7

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$