# How do you solve the following system?:  -2x+3y=5, -x+y=-3

Jun 28, 2017

$x = 14 , y - 11$

#### Explanation:

$\textcolor{w h i t e}{+} - 2 x + 3 y = 5$
$\textcolor{w h i t e}{+}$
$\textcolor{w h i t e}{+} - x + y = - 3$

Let's use substitution! We need to solve for $y$ in the second equation:
$- x + y = - 3$

$y = - 3 + x$

Let's substitute $\left(- 3 + x\right)$ for $y$ in the first equation

$- 2 x + 3 y = 5$

$- 2 x + 3 \left(- 3 + x\right) = 5$

$- 2 x - 9 + 3 x = 5$

$x = 14$

Now we have $x$, let's solve for $y$:

$- 2 \left(14\right) + 3 y = 5$

$- 28 + 3 y = 5$

$3 y = 33$

$y = 11$

Now we have our solutions, but to double-check, let's solve the second equation, using $14$ and $11$ for $x$ and $y$:

$- x + y = - 3$

$- \left(14\right) + 11$ should give us $- 3$, if we did everything correctly

$- 3 = - 3$, so we were right!