# Question #d8ac3

Apr 10, 2017

$x = 3$, $y = 0$

#### Explanation:

$\textcolor{w h i t e}{+} - 4 x + 2 y = - 12$
$\textcolor{w h i t e}{+}$
$\textcolor{w h i t e}{+} \textcolor{w h i t e}{-} 3 x + 2 y = 9$

We need to eliminate one of the variables. The $y$s are already equal, so we will subtract the two equations and remove $2 y$:

$\textcolor{w h i t e}{+} - 4 x + \cancel{2 y} = - 12$
$\textcolor{b l a c k}{-}$
$\textcolor{w h i t e}{+} \textcolor{w h i t e}{-} 3 x + \cancel{2 y} = \textcolor{w h i t e}{-} 9$
...............................................................
$- 7 x = - 21$

Now we just solve for $x$

$- 7 x = - 21$
Divide by $7$ on both sides
$x = \frac{- 21}{-} 7$ or $x = 3$

Now we have $x$; we need to find the value of $y$. To do that, we pick an equation and solve for $y$, substituting $x$ for $3$.

$3 x + 2 y = 9$
$3 \left(3\right) + y = 9$
$9 + y = 9$
$9 + y \textcolor{p u r p \le}{- 9} = 9 \textcolor{p u r p \le}{- 9}$
$y = 0$

Just to double check our work, let's solve the second equation using both $x$ and $y$ as $3$ and $0$, respectively.

$- 4 x + 2 y = - 12$
$- 4 \left(3\right) + 2 \left(0\right)$ should equal $- 12$
$- 12 + 0 = - 12$
We were right! Congratulations. Nice work.