Algebra Examples

$4 x = 2 y + 18$ $x - 8 y = 12$

Step 1

Divide each term in $4 x = 2 y + 18$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 x = 2 y + 18$ by $4$ .

$\frac{4 x}{4} = \frac{2 y}{4} + \frac{18}{4}$

$x - 8 y = 12$

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.

$\frac{4 x}{4} = \frac{2 y}{4} + \frac{18}{4}$

$x - 8 y = 12$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{2 y}{4} + \frac{18}{4}$

$x - 8 y = 12$

$x = \frac{2 y}{4} + \frac{18}{4}$

$x - 8 y = 12$

$x = \frac{2 y}{4} + \frac{18}{4}$

$x - 8 y = 12$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $2$ and $4$ .

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Step 1.3.1.1.1

Factor $2$ out of $2 y$ .

$x = \frac{2 (y)}{4} + \frac{18}{4}$

$x - 8 y = 12$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 y}{2 \cdot 2} + \frac{18}{4}$

$x - 8 y = 12$

Step 1.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 y}{2 \cdot 2} + \frac{18}{4}$

$x - 8 y = 12$

Step 1.3.1.1.2.3

Rewrite the expression.

$x = \frac{y}{2} + \frac{18}{4}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{18}{4}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{18}{4}$

$x - 8 y = 12$

Step 1.3.1.2

Cancel the common factor of $18$ and $4$ .

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Step 1.3.1.2.1

Factor $2$ out of $18$ .

$x = \frac{y}{2} + \frac{2 (9)}{4}$

$x - 8 y = 12$

Step 1.3.1.2.2

Cancel the common factors.

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Step 1.3.1.2.2.1

Factor $2$ out of $4$ .

$x = \frac{y}{2} + \frac{2 \cdot 9}{2 \cdot 2}$

$x - 8 y = 12$

Step 1.3.1.2.2.2

Cancel the common factor.

$x = \frac{y}{2} + \frac{2 \cdot 9}{2 \cdot 2}$

$x - 8 y = 12$

Step 1.3.1.2.2.3

Rewrite the expression.

$x = \frac{y}{2} + \frac{9}{2}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$x - 8 y = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$x - 8 y = 12$

Step 2

Replace all occurrences of $x$ with $\frac{y}{2} + \frac{9}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x - 8 y = 12$ with $\frac{y}{2} + \frac{9}{2}$ .

$(\frac{y}{2} + \frac{9}{2}) - 8 y = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $(\frac{y}{2} + \frac{9}{2}) - 8 y$ .

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Step 2.2.1.1

To write $- 8 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{2} - 8 y \cdot \frac{2}{2} + \frac{9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.2

Combine $- 8 y$ and $\frac{2}{2}$ .

$\frac{y}{2} + \frac{- 8 y \cdot 2}{2} + \frac{9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.3

Combine the numerators over the common denominator.

$\frac{y - 8 y \cdot 2}{2} + \frac{9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{y - 8 y \cdot 2 + 9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.5

Multiply $2$ by $- 8$ .

$\frac{y - 16 y + 9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.6

Subtract $16 y$ from $y$ .

$\frac{- 15 y + 9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.7

Factor $3$ out of $- 15 y + 9$ .

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Step 2.2.1.7.1

Factor $3$ out of $- 15 y$ .

$\frac{3 (- 5 y) + 9}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.7.2

Factor $3$ out of $9$ .

$\frac{3 (- 5 y) + 3 (3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.7.3

Factor $3$ out of $3 (- 5 y) + 3 (3)$ .

$\frac{3 (- 5 y + 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$\frac{3 (- 5 y + 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.8

Factor $- 1$ out of $- 5 y$ .

$\frac{3 (- (5 y) + 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.9

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{3 (- (5 y) - 1 \cdot - 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.10

Factor $- 1$ out of $- (5 y) - 1 (- 3)$ .

$\frac{3 (- (5 y - 3))}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.11

Simplify the expression.

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Step 2.2.1.11.1

Rewrite $- (5 y - 3)$ as $- 1 (5 y - 3)$ .

$\frac{3 (- 1 (5 y - 3))}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 2.2.1.11.2

Move the negative in front of the fraction.

$- \frac{3 (5 y - 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$- \frac{3 (5 y - 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$- \frac{3 (5 y - 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$- \frac{3 (5 y - 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

$- \frac{3 (5 y - 3)}{2} = 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3

Solve for $y$ in $- \frac{3 (5 y - 3)}{2} = 12$ .

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Step 3.1

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

$- \frac{2}{3} \cdot (- \frac{3 (5 y - 3)}{2}) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2

Simplify both sides of the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $- \frac{2}{3} (- \frac{3 (5 y - 3)}{2})$ .

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Step 3.2.1.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot (- \frac{3 (5 y - 3)}{2}) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.1.2

Move the leading negative in $- \frac{3 (5 y - 3)}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 (5 y - 3)}{2} = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 (5 y - 3)}{2} = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 (5 y - 3)}{2} = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} \cdot (- 3 (5 y - 3)) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

$\frac{- 1}{3} \cdot (- 3 (5 y - 3)) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.1.2.1

Factor $3$ out of $- 3 (5 y - 3)$ .

$\frac{- 1}{3} \cdot (3 (- (5 y - 3))) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} \cdot (3 (- (5 y - 3))) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.2.3

Rewrite the expression.

$5 y - 3 = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (5 y - 3) = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.1.1.3.2

Multiply $5 y - 3$ by $1$ .

$5 y - 3 = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - \frac{2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $- \frac{2}{3} \cdot 12$ .

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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

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$5 y - 3 = \frac{- 2}{3} \cdot 12$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.2.1.1.2

Factor $3$ out of $12$ .

$5 y - 3 = \frac{- 2}{3} \cdot (3 (4))$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.2.1.1.3

Cancel the common factor.

$5 y - 3 = \frac{- 2}{3} \cdot (3 \cdot 4)$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.2.1.1.4

Rewrite the expression.

$5 y - 3 = - 2 \cdot 4$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - 2 \cdot 4$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.2.2.1.2

Multiply $- 2$ by $4$ .

$5 y - 3 = - 8$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - 8$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - 8$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y - 3 = - 8$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.3

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

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Step 3.3.1

Add $3$ to both sides of the equation.

$5 y = - 8 + 3$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.3.2

Add $- 8$ and $3$ .

$5 y = - 5$

$x = \frac{y}{2} + \frac{9}{2}$

$5 y = - 5$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.4

Divide each term in $5 y = - 5$ by $5$ and simplify.

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Step 3.4.1

Divide each term in $5 y = - 5$ by $5$ .

$\frac{5 y}{5} = \frac{- 5}{5}$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $5$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 5}{5}$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{5}$

$x = \frac{y}{2} + \frac{9}{2}$

$y = \frac{- 5}{5}$

$x = \frac{y}{2} + \frac{9}{2}$

$y = \frac{- 5}{5}$

$x = \frac{y}{2} + \frac{9}{2}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $- 5$ by $5$ .

$y = - 1$

$x = \frac{y}{2} + \frac{9}{2}$

$y = - 1$

$x = \frac{y}{2} + \frac{9}{2}$

$y = - 1$

$x = \frac{y}{2} + \frac{9}{2}$

$y = - 1$

$x = \frac{y}{2} + \frac{9}{2}$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{y}{2} + \frac{9}{2}$ with $- 1$ .

$x = \frac{- 1}{2} + \frac{9}{2}$

$y = - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{- 1}{2} + \frac{9}{2}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 1 + 9}{2}$

$y = - 1$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Add $- 1$ and $9$ .

$x = \frac{8}{2}$

$y = - 1$

Step 4.2.1.2.2

Divide $8$ by $2$ .

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

Step 5

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

$(4, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 7