Algebra Examples

$4 y = x + 8$ $x = \frac{2}{3} y + 2$

Step 1

Divide each term in $4 y = x + 8$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 y = x + 8$ by $4$ .

$\frac{4 y}{4} = \frac{x}{4} + \frac{8}{4}$

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{x}{4} + \frac{8}{4}$

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

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{4} + \frac{8}{4}$

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

$y = \frac{x}{4} + \frac{8}{4}$

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

$y = \frac{x}{4} + \frac{8}{4}$

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $8$ by $4$ .

$y = \frac{x}{4} + 2$

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

$y = \frac{x}{4} + 2$

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

$y = \frac{x}{4} + 2$

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

Step 2

Rewrite the equation as $\frac{2}{3} y + 2 = x$ .

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

$y = \frac{x}{4} + 2$

Step 3

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

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

$y = \frac{x}{4} + 2$

Step 4

Subtract $2$ from both sides of the equation.

$\frac{2 y}{3} = x - 2$

$y = \frac{x}{4} + 2$

Step 5

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{2} \cdot (2 y) = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

$\frac{1}{2} \cdot (2 y) = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

Step 6.1.1.2

Cancel the common factor of $2$ .

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Step 6.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} \cdot (2 (y)) = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 y) = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

Step 6.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

$y = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

$y = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

$y = \frac{3}{2} \cdot (x - 2)$

$y = \frac{x}{4} + 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{3}{2} (x - 2)$ .

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Step 6.2.1.1

Apply the distributive property.

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

$y = \frac{x}{4} + 2$

Step 6.2.1.2

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

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

$y = \frac{x}{4} + 2$

Step 6.2.1.3

Cancel the common factor of $2$ .

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Step 6.2.1.3.1

Factor $2$ out of $- 2$ .

$y = \frac{3 x}{2} + \frac{3}{2} \cdot (2 (- 1))$

$y = \frac{x}{4} + 2$

Step 6.2.1.3.2

Cancel the common factor.

$y = \frac{3 x}{2} + \frac{3}{2} \cdot (2 \cdot - 1)$

$y = \frac{x}{4} + 2$

Step 6.2.1.3.3

Rewrite the expression.

$y = \frac{3 x}{2} + 3 \cdot - 1$

$y = \frac{x}{4} + 2$

$y = \frac{3 x}{2} + 3 \cdot - 1$

$y = \frac{x}{4} + 2$

Step 6.2.1.4

Multiply $3$ by $- 1$ .

$y = \frac{3 x}{2} - 3$

$y = \frac{x}{4} + 2$

$y = \frac{3 x}{2} - 3$

$y = \frac{x}{4} + 2$

$y = \frac{3 x}{2} - 3$

$y = \frac{x}{4} + 2$

$y = \frac{3 x}{2} - 3$

$y = \frac{x}{4} + 2$

Step 7

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(4, 3)$

Step 8