Solve the System of Equations y=-2x-9 2x+3y=-3

$y = - 2 x - 9$ $2 x + 3 y = - 3$

Step 1

Replace all occurrences of $y$ with $- 2 x - 9$ in each equation.

Replace all occurrences of $y$ in $2 x + 3 y = - 3$ with $- 2 x - 9$ .

$2 x + 3 (- 2 x - 9) = - 3$

$y = - 2 x - 9$

Simplify the left side.

Simplify $2 x + 3 (- 2 x - 9)$ .

Simplify each term.

Apply the distributive property.

$2 x + 3 (- 2 x) + 3 \cdot - 9 = - 3$

$y = - 2 x - 9$

Multiply $- 2$ by $3$ .

$2 x - 6 x + 3 \cdot - 9 = - 3$

$y = - 2 x - 9$

Multiply $3$ by $- 9$ .

$2 x - 6 x - 27 = - 3$

$y = - 2 x - 9$

$2 x - 6 x - 27 = - 3$

$y = - 2 x - 9$

Subtract $6 x$ from $2 x$ .

$- 4 x - 27 = - 3$

$y = - 2 x - 9$

$- 4 x - 27 = - 3$

$y = - 2 x - 9$

$- 4 x - 27 = - 3$

$y = - 2 x - 9$

$- 4 x - 27 = - 3$

$y = - 2 x - 9$

Step 2

Solve for $x$ in $- 4 x - 27 = - 3$ .

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

Add $27$ to both sides of the equation.

$- 4 x = - 3 + 27$

$y = - 2 x - 9$

Add $- 3$ and $27$ .

$- 4 x = 24$

$y = - 2 x - 9$

$- 4 x = 24$

$y = - 2 x - 9$

Divide each term in $- 4 x = 24$ by $- 4$ and simplify.

Divide each term in $- 4 x = 24$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{24}{- 4}$

$y = - 2 x - 9$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{24}{- 4}$

$y = - 2 x - 9$

Divide $x$ by $1$ .

$x = \frac{24}{- 4}$

$y = - 2 x - 9$

$x = \frac{24}{- 4}$

$y = - 2 x - 9$

$x = \frac{24}{- 4}$

$y = - 2 x - 9$

Simplify the right side.

Divide $24$ by $- 4$ .

$x = - 6$

$y = - 2 x - 9$

$x = - 6$

$y = - 2 x - 9$

$x = - 6$

$y = - 2 x - 9$

$x = - 6$

$y = - 2 x - 9$

Step 3

Replace all occurrences of $x$ with $- 6$ in each equation.

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

$y = - 2 \cdot - 6 - 9$

$x = - 6$

Simplify the right side.

Simplify $- 2 \cdot - 6 - 9$ .

Multiply $- 2$ by $- 6$ .

$y = 12 - 9$

$x = - 6$

Subtract $9$ from $12$ .

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

Step 4

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

$(- 6, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 6, 3)$

Equation Form:

$x = - 6, y = 3$

Step 6

Solve the System of Equations y=-2x-9 2x+3y=-3

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