# Question 4e3ef

Apr 11, 2017

$x = 7$, $y = - 16$

#### Explanation:

$\textcolor{w h i t e}{-} x + y = - 9$
$\textcolor{w h i t e}{-}$
$x + 2 y = - 25$

Let's use elimination here. We can subtract both equations to remove the $x$:
$\textcolor{w h i t e}{-} \cancel{x} + y = - 9$
$\textcolor{b l a c k}{-}$
$\cancel{x} + 2 y = - 25$
.......................................
$- y = 16$
$y = - 16$

Now let's solve for $x$ by replacing $y$ with $- 160.$
$x + y = - 9$
$x + \left(- 16\right) = - 9$
Add $16$ on both sides
$x = 7$

Just to double check our work, we'll solve the second problem using $7$ and $- 16$ for $x$ and $y$, respectively.
$x + 2 y = - 25$
$7 + 2 \cdot \left(- 16\right)$ should equal $- 25$
$7 - 32 = 12$
$12 = 12$
We were right! Good job!

Apr 11, 2017

color(blue)(x=7

#### Explanation:

$x + y = - 9 - - - - - \left(1\right)$

$x + 2 y = - 25 - - - - - \left(2\right)$

$\left(1\right) \times 2$$2 x + 2 y = - 18 - - - - \left(3\right)$

$\left(2\right) - \left(3\right)$$- x = - 7$

color(blue)(x=7

sustitute $x = 7$ in $\left(2\right)$

$7 + 2 y = - 25$

$2 y = - 25 - 7$

$2 y = - 32$

$y = - \frac{32}{2}$

$y = - 16$

Check:

substitute color(blue)(x=7 and color(blue)(y=-16 # in $\left(1\right)$

$\textcolor{b l u e}{7} + \left(\textcolor{b l u e}{-} 16\right) = - 9$

$- 9 = - 9$