# How do you solve 4x+3y=-7 and 5x-2y=-26?

May 6, 2016

Combine the equations to eliminate $y$ and solve for $x$. Then substitute the value found for $x$ and solve for $y$ to find:

$\left\{\begin{matrix}x = - 4 \\ y = 3\end{matrix}\right.$

#### Explanation:

Multiply the first equation by $2$ and the second by $3$ to get:

$\left\{\begin{matrix}8 x + 6 y = - 14 \\ 15 x - 6 y = - 78\end{matrix}\right.$

Add these two equations together to get:

$23 x = - 92$

Divide both sides by $23$ to get:

$x = - 4$

Substitute this value of $x$ in the first given equation to get:

$- 7 = 4 \left(- 4\right) + 3 y = - 16 + 3 y$

Add $16$ to both ends and transpose to get:

$3 y = 9$

Divide both sides by $3$ to get:

$y = 3$