Solve the System of Equations 8x+2y=-12 and 5x-y=4

$8 x + 2 y = - 12$ and $5 x - y = 4$

Solve for $x$ in $8 x + 2 y = - 12$ .

Subtract $2 y$ from both sides of the equation.

$8 x = - 12 - 2 y$

$5 x - y = 4$

Divide each term in $8 x = - 12 - 2 y$ by $8$ and simplify.

Divide each term in $8 x = - 12 - 2 y$ by $8$ .

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

$5 x - y = 4$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

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

$5 x - y = 4$

Divide $x$ by $1$ .

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

$5 x - y = 4$

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

$5 x - y = 4$

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

$5 x - y = 4$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 12$ and $8$ .

Factor $4$ out of $- 12$ .

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

$5 x - y = 4$

Cancel the common factors.

Factor $4$ out of $8$ .

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

$5 x - y = 4$

Cancel the common factor.

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

$5 x - y = 4$

Rewrite the expression.

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

$5 x - y = 4$

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

$5 x - y = 4$

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

$5 x - y = 4$

Move the negative in front of the fraction.

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

$5 x - y = 4$

Cancel the common factor of $- 2$ and $8$ .

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

$x = - \frac{3}{2} + \frac{2 (- y)}{8}$

$5 x - y = 4$

Cancel the common factors.

Factor $2$ out of $8$ .

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

$5 x - y = 4$

Cancel the common factor.

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

$5 x - y = 4$

Rewrite the expression.

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

$5 x - y = 4$

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

$5 x - y = 4$

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

$5 x - y = 4$

Move the negative in front of the fraction.

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

$5 x - y = 4$

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

$5 x - y = 4$

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

$5 x - y = 4$

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

$5 x - y = 4$

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

$5 x - y = 4$

Replace all occurrences of $x$ with $- \frac{3}{2} - \frac{y}{4}$ in each equation.

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

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

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

Simplify the left side.

Simplify $5 (- \frac{3}{2} - \frac{y}{4}) - y$ .

Simplify each term.

Apply the distributive property.

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

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

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

Multiply $- 1$ by $5$ .

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

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

Combine $- 5$ and $\frac{3}{2}$ .

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

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

Multiply $- 5$ by $3$ .

$\frac{- 15}{2} + 5 (- \frac{y}{4}) - y = 4$

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

$\frac{- 15}{2} + 5 (- \frac{y}{4}) - y = 4$

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

Multiply $5 (- \frac{y}{4})$ .

Multiply $- 1$ by $5$ .

$\frac{- 15}{2} - 5 \frac{y}{4} - y = 4$

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

Combine $- 5$ and $\frac{y}{4}$ .

$\frac{- 15}{2} + \frac{- 5 y}{4} - y = 4$

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

$\frac{- 15}{2} + \frac{- 5 y}{4} - y = 4$

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

Simplify each term.

Move the negative in front of the fraction.

$- \frac{15}{2} + \frac{- 5 y}{4} - y = 4$

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

Move the negative in front of the fraction.

$- \frac{15}{2} - \frac{5 y}{4} - y = 4$

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

$- \frac{15}{2} - \frac{5 y}{4} - y = 4$

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

$- \frac{15}{2} - \frac{5 y}{4} - y = 4$

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

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

$- \frac{15}{2} - \frac{5 y}{4} - y \cdot \frac{4}{4} = 4$

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

Simplify terms.

Combine $- y$ and $\frac{4}{4}$ .

$- \frac{15}{2} - \frac{5 y}{4} + \frac{- y \cdot 4}{4} = 4$

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

Combine the numerators over the common denominator.

$- \frac{15}{2} + \frac{- 5 y - y \cdot 4}{4} = 4$

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

$- \frac{15}{2} + \frac{- 5 y - y \cdot 4}{4} = 4$

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

Simplify each term.

Simplify the numerator.

Factor $y$ out of $- 5 y - y \cdot 4$ .

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

$- \frac{15}{2} + \frac{y \cdot - 5 - y \cdot 4}{4} = 4$

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

Factor $y$ out of $- y \cdot 4$ .

$- \frac{15}{2} + \frac{y \cdot - 5 + y (- 1 \cdot 4)}{4} = 4$

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

Factor $y$ out of $y \cdot - 5 + y (- 1 \cdot 4)$ .

$- \frac{15}{2} + \frac{y (- 5 - 1 \cdot 4)}{4} = 4$

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

$- \frac{15}{2} + \frac{y (- 5 - 1 \cdot 4)}{4} = 4$

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

Multiply $- 1$ by $4$ .

$- \frac{15}{2} + \frac{y (- 5 - 4)}{4} = 4$

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

Subtract $4$ from $- 5$ .

$- \frac{15}{2} + \frac{y \cdot - 9}{4} = 4$

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

$- \frac{15}{2} + \frac{y \cdot - 9}{4} = 4$

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

Move $- 9$ to the left of $y$ .

$- \frac{15}{2} + \frac{- 9 \cdot y}{4} = 4$

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

Move the negative in front of the fraction.

$- \frac{15}{2} - \frac{9 y}{4} = 4$

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

$- \frac{15}{2} - \frac{9 y}{4} = 4$

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

$- \frac{15}{2} - \frac{9 y}{4} = 4$

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

$- \frac{15}{2} - \frac{9 y}{4} = 4$

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

$- \frac{15}{2} - \frac{9 y}{4} = 4$

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

Solve for $y$ in $- \frac{15}{2} - \frac{9 y}{4} = 4$ .

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

Add $\frac{15}{2}$ to both sides of the equation.

$- \frac{9 y}{4} = 4 + \frac{15}{2}$

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

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9 y}{4} = 4 \cdot \frac{2}{2} + \frac{15}{2}$

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

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

$- \frac{9 y}{4} = \frac{4 \cdot 2}{2} + \frac{15}{2}$

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

Combine the numerators over the common denominator.

$- \frac{9 y}{4} = \frac{4 \cdot 2 + 15}{2}$

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

Simplify the numerator.

Multiply $4$ by $2$ .

$- \frac{9 y}{4} = \frac{8 + 15}{2}$

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

Add $8$ and $15$ .

$- \frac{9 y}{4} = \frac{23}{2}$

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

$- \frac{9 y}{4} = \frac{23}{2}$

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

$- \frac{9 y}{4} = \frac{23}{2}$

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

Multiply both sides of the equation by $- \frac{4}{9}$ .

$- \frac{4}{9} \cdot (- \frac{9 y}{4}) = - \frac{4}{9} \cdot \frac{23}{2}$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{9} (- \frac{9 y}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$\frac{- 4}{9} \cdot (- \frac{9 y}{4}) = - \frac{4}{9} \cdot \frac{23}{2}$

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

Move the leading negative in $- \frac{9 y}{4}$ into the numerator.

$\frac{- 4}{9} \cdot \frac{- 9 y}{4} = - \frac{4}{9} \cdot \frac{23}{2}$

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

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{9} \cdot \frac{- 9 y}{4} = - \frac{4}{9} \cdot \frac{23}{2}$

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

Cancel the common factor.

$\frac{4 \cdot - 1}{9} \cdot \frac{- 9 y}{4} = - \frac{4}{9} \cdot \frac{23}{2}$

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

Rewrite the expression.

$\frac{- 1}{9} \cdot (- 9 y) = - \frac{4}{9} \cdot \frac{23}{2}$

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

$\frac{- 1}{9} \cdot (- 9 y) = - \frac{4}{9} \cdot \frac{23}{2}$

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

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 y$ .

$\frac{- 1}{9} \cdot (9 (- y)) = - \frac{4}{9} \cdot \frac{23}{2}$

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

Cancel the common factor.

$\frac{- 1}{9} \cdot (9 (- y)) = - \frac{4}{9} \cdot \frac{23}{2}$

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

Rewrite the expression.

$y = - \frac{4}{9} \cdot \frac{23}{2}$

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

$y = - \frac{4}{9} \cdot \frac{23}{2}$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{4}{9} \cdot \frac{23}{2}$

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

Multiply $y$ by $1$ .

$y = - \frac{4}{9} \cdot \frac{23}{2}$

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

$y = - \frac{4}{9} \cdot \frac{23}{2}$

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

$y = - \frac{4}{9} \cdot \frac{23}{2}$

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

$y = - \frac{4}{9} \cdot \frac{23}{2}$

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

Simplify the right side.

Simplify $- \frac{4}{9} \cdot \frac{23}{2}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$y = \frac{- 4}{9} \cdot \frac{23}{2}$

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

Factor $2$ out of $- 4$ .

$y = \frac{2 (- 2)}{9} \cdot \frac{23}{2}$

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

Cancel the common factor.

$y = \frac{2 \cdot - 2}{9} \cdot \frac{23}{2}$

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

Rewrite the expression.

$y = \frac{- 2}{9} \cdot 23$

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

$y = \frac{- 2}{9} \cdot 23$

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

Combine $\frac{- 2}{9}$ and $23$ .

$y = \frac{- 2 \cdot 23}{9}$

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

Simplify the expression.

Multiply $- 2$ by $23$ .

$y = \frac{- 46}{9}$

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

Move the negative in front of the fraction.

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

Replace all occurrences of $y$ with $- \frac{46}{9}$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{3}{2} - \frac{y}{4}$ with $- \frac{46}{9}$ .

$x = - \frac{3}{2} - \frac{- \frac{46}{9}}{4}$

$y = - \frac{46}{9}$

Simplify the right side.

Simplify $- \frac{3}{2} - \frac{- \frac{46}{9}}{4}$ .

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3}{2} - (- \frac{46}{9} \cdot \frac{1}{4})$

$y = - \frac{46}{9}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{46}{9}$ into the numerator.

$x = - \frac{3}{2} - (\frac{- 46}{9} \cdot \frac{1}{4})$

$y = - \frac{46}{9}$

Factor $2$ out of $- 46$ .

$x = - \frac{3}{2} - (\frac{2 (- 23)}{9} \cdot \frac{1}{4})$

$y = - \frac{46}{9}$

Factor $2$ out of $4$ .

$x = - \frac{3}{2} - (\frac{2 \cdot - 23}{9} \cdot \frac{1}{2 \cdot 2})$

$y = - \frac{46}{9}$

Cancel the common factor.

$x = - \frac{3}{2} - (\frac{2 \cdot - 23}{9} \cdot \frac{1}{2 \cdot 2})$

$y = - \frac{46}{9}$

Rewrite the expression.

$x = - \frac{3}{2} - (\frac{- 23}{9} \cdot \frac{1}{2})$

$y = - \frac{46}{9}$

$x = - \frac{3}{2} - (\frac{- 23}{9} \cdot \frac{1}{2})$

$y = - \frac{46}{9}$

Multiply $\frac{- 23}{9}$ by $\frac{1}{2}$ .

$x = - \frac{3}{2} - \frac{- 23}{9 \cdot 2}$

$y = - \frac{46}{9}$

Multiply $9$ by $2$ .

$x = - \frac{3}{2} - \frac{- 23}{18}$

$y = - \frac{46}{9}$

Move the negative in front of the fraction.

$x = - \frac{3}{2} + \frac{23}{18}$

$y = - \frac{46}{9}$

Multiply $- - \frac{23}{18}$ .

Multiply $- 1$ by $- 1$ .

$x = - \frac{3}{2} + 1 (\frac{23}{18})$

$y = - \frac{46}{9}$

Multiply $\frac{23}{18}$ by $1$ .

$x = - \frac{3}{2} + \frac{23}{18}$

$y = - \frac{46}{9}$

$x = - \frac{3}{2} + \frac{23}{18}$

$y = - \frac{46}{9}$

$x = - \frac{3}{2} + \frac{23}{18}$

$y = - \frac{46}{9}$

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$x = - \frac{3}{2} \cdot \frac{9}{9} + \frac{23}{18}$

$y = - \frac{46}{9}$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{9}{9}$ .

$x = - \frac{3 \cdot 9}{2 \cdot 9} + \frac{23}{18}$

$y = - \frac{46}{9}$

Multiply $2$ by $9$ .

$x = - \frac{3 \cdot 9}{18} + \frac{23}{18}$

$y = - \frac{46}{9}$

$x = - \frac{3 \cdot 9}{18} + \frac{23}{18}$

$y = - \frac{46}{9}$

Combine the numerators over the common denominator.

$x = \frac{- 3 \cdot 9 + 23}{18}$

$y = - \frac{46}{9}$

Simplify the numerator.

Multiply $- 3$ by $9$ .

$x = \frac{- 27 + 23}{18}$

$y = - \frac{46}{9}$

Add $- 27$ and $23$ .

$x = \frac{- 4}{18}$

$y = - \frac{46}{9}$

$x = \frac{- 4}{18}$

$y = - \frac{46}{9}$

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

Factor $2$ out of $- 4$ .

$x = \frac{2 (- 2)}{18}$

$y = - \frac{46}{9}$

Cancel the common factors.

Factor $2$ out of $18$ .

$x = \frac{2 \cdot - 2}{2 \cdot 9}$

$y = - \frac{46}{9}$

Cancel the common factor.

$x = \frac{2 \cdot - 2}{2 \cdot 9}$

$y = - \frac{46}{9}$

Rewrite the expression.

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

Move the negative in front of the fraction.

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$y = - \frac{46}{9}$

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

$(- \frac{2}{9}, - \frac{46}{9})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{2}{9}, - \frac{46}{9})$

Equation Form:

$x = - \frac{2}{9}, y = - \frac{46}{9}$

Solve the System of Equations 8x+2y=-12 and 5x-y=4

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