Solve the System of Equations -x+2y=-4 and -6x+9y=-12

$- x + 2 y = - 4$ and $- 6 x + 9 y = - 12$

Solve for $x$ in $- x + 2 y = - 4$ .

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

$- x = - 4 - 2 y$

$- 6 x + 9 y = - 12$

Divide each term in $- x = - 4 - 2 y$ by $- 1$ and simplify.

Divide each term in $- x = - 4 - 2 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1} + \frac{- 2 y}{- 1}$

$- 6 x + 9 y = - 12$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1} + \frac{- 2 y}{- 1}$

$- 6 x + 9 y = - 12$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1} + \frac{- 2 y}{- 1}$

$- 6 x + 9 y = - 12$

$x = \frac{- 4}{- 1} + \frac{- 2 y}{- 1}$

$- 6 x + 9 y = - 12$

Simplify the right side.

Simplify each term.

Divide $- 4$ by $- 1$ .

$x = 4 + \frac{- 2 y}{- 1}$

$- 6 x + 9 y = - 12$

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$x = 4 - 1 \cdot (- 2 y)$

$- 6 x + 9 y = - 12$

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$x = 4 - (- 2 y)$

$- 6 x + 9 y = - 12$

Multiply $- 2$ by $- 1$ .

$x = 4 + 2 y$

$- 6 x + 9 y = - 12$

$x = 4 + 2 y$

$- 6 x + 9 y = - 12$

$x = 4 + 2 y$

$- 6 x + 9 y = - 12$

$x = 4 + 2 y$

$- 6 x + 9 y = - 12$

$x = 4 + 2 y$

$- 6 x + 9 y = - 12$

Replace all occurrences of $x$ with $4 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- 6 x + 9 y = - 12$ with $4 + 2 y$ .

$- 6 (4 + 2 y) + 9 y = - 12$

$x = 4 + 2 y$

Simplify the left side.

Simplify $- 6 (4 + 2 y) + 9 y$ .

Simplify each term.

Apply the distributive property.

$- 6 \cdot 4 - 6 (2 y) + 9 y = - 12$

$x = 4 + 2 y$

Multiply $- 6$ by $4$ .

$- 24 - 6 (2 y) + 9 y = - 12$

$x = 4 + 2 y$

Multiply $2$ by $- 6$ .

$- 24 - 12 y + 9 y = - 12$

$x = 4 + 2 y$

$- 24 - 12 y + 9 y = - 12$

$x = 4 + 2 y$

Add $- 12 y$ and $9 y$ .

$- 24 - 3 y = - 12$

$x = 4 + 2 y$

$- 24 - 3 y = - 12$

$x = 4 + 2 y$

$- 24 - 3 y = - 12$

$x = 4 + 2 y$

$- 24 - 3 y = - 12$

$x = 4 + 2 y$

Solve for $y$ in $- 24 - 3 y = - 12$ .

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

Add $24$ to both sides of the equation.

$- 3 y = - 12 + 24$

$x = 4 + 2 y$

Add $- 12$ and $24$ .

$- 3 y = 12$

$x = 4 + 2 y$

$- 3 y = 12$

$x = 4 + 2 y$

Divide each term in $- 3 y = 12$ by $- 3$ and simplify.

Divide each term in $- 3 y = 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

$x = 4 + 2 y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

$x = 4 + 2 y$

Divide $y$ by $1$ .

$y = \frac{12}{- 3}$

$x = 4 + 2 y$

$y = \frac{12}{- 3}$

$x = 4 + 2 y$

$y = \frac{12}{- 3}$

$x = 4 + 2 y$

Simplify the right side.

Divide $12$ by $- 3$ .

$y = - 4$

$x = 4 + 2 y$

$y = - 4$

$x = 4 + 2 y$

$y = - 4$

$x = 4 + 2 y$

$y = - 4$

$x = 4 + 2 y$

Replace all occurrences of $y$ with $- 4$ in each equation.

Replace all occurrences of $y$ in $x = 4 + 2 y$ with $- 4$ .

$x = 4 + 2 (- 4)$

$y = - 4$

Simplify the right side.

Simplify $4 + 2 (- 4)$ .

Multiply $2$ by $- 4$ .

$x = 4 - 8$

$y = - 4$

Subtract $8$ from $4$ .

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

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

$(- 4, - 4)$

The result can be shown in multiple forms.

Point Form:

$(- 4, - 4)$

Equation Form:

$x = - 4, y = - 4$

Solve the System of Equations -x+2y=-4 and -6x+9y=-12

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