# How do you solve 3x+4y=22 and x-5y=-37?

##### 1 Answer
Sep 9, 2015

The solution for the system of equations is
color(blue)(x=-2, y=7

#### Explanation:

$\textcolor{b l u e}{3 x} + 4 y = 22$...........equation $\left(1\right)$

$x - 5 y = - 37$, multiplying this equation by $3$
$\textcolor{b l u e}{3 x} - 15 y = - 111$....equation $\left(2\right)$

Now we can solve using the method of elimination .

Subtracting equation $2$ from $1$ eliminates color(blue)(3x

$\textcolor{b l u e}{3 x} + 4 y = 22$
$- \cancel{\textcolor{b l u e}{3 x}} + 15 y = + 111$

$19 y = 133$
color(blue)(y=7

Now we find $x$ by substituting $y$ in equation $1$
$3 x + 4 y = 22$

$3 x = 22 - 4 y$

$3 x = 22 - 4 \cdot 7$

$3 x = 22 - 28$

$3 x = - 6$
color(blue)(x=-2