# How do you solve -2x-9y=-25 and -4x-9y=-23?

Sep 5, 2015

I found:
$x = - 1$
$y = 3$

#### Explanation:

I would add together the two equations (in columns) after multiplying the first by $- 1$ to get:
$\left\{\begin{matrix}\textcolor{red}{2 x + 9 y = 25} \\ - 4 x - 9 y = - 23\end{matrix}\right.$ add together:
$- 2 x + 0 = 2$
$x = \frac{2}{-} 2 = - 1$
Substitute into the first equation:
$2 - 9 y = - 25$
$- 9 y = - 27$
$y = \frac{27}{9} = 3$

Sep 5, 2015

$\left\{\begin{matrix}x = - 1 \\ y = 3\end{matrix}\right.$

#### Explanation:

Your system of equations looks like this

$\left\{\begin{matrix}- 2 x - 9 y = - 25 \\ - 4 x - 9 y = - 23\end{matrix}\right.$

Multiply the first equation by $\left(- 1\right)$ to get

$- 2 x - 9 y = - 25 | \cdot \left(- 1\right)$

$2 x + 9 y = 25$

The system now looks like this

$\left\{\begin{matrix}2 x + 9 y = 25 \\ - 4 x - 9 y = - 23\end{matrix}\right.$

Add the left-hand sides and the right-hand sides of the two equations seprately to get

$2 x + \textcolor{red}{\cancel{\textcolor{b l a c k}{9 y}}} - 4 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{9 y}}} = 25 - 23$

$- 2 x = 2 \implies x = \frac{2}{\left(- 2\right)} = - 1$

Take this value of $x$ into one of the two equations to get the value of $y$

$- 2 \cdot \left(- 1\right) - 9 y = - 25$

$2 - 9 y = - 25$

$- 9 y = - 27 \implies y = \frac{\left(- 27\right)}{\left(- 9\right)} = 3$

The solution set to this system of equations is $x = - 1$ and $y = 3$.