# How do you solve –2x – 3y = –17 and x + 4y = 16?

Apr 22, 2018

$x = 4 , y = 3$

#### Explanation:

$- 2 x - 3 y = - 17$

$- 2 x \textcolor{red}{\cancel{\textcolor{b l a c k}{- 3 y} + 3 y}} = - 17 \textcolor{red}{+ 3 y}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} x}{\textcolor{red}{\cancel{- 2}}} = \frac{3 y - 17}{\textcolor{red}{- 2}}$

$x = \frac{3 y - 17}{-} 2$

____$\textcolor{w h i t e}{.}$

$x + 4 y = 16$

$x \textcolor{red}{\cancel{\textcolor{b l a c k}{+ 4 y} - 4 y}} = 16 \textcolor{red}{- 4 y}$

Now we can graph both of these equations on a graph and see where they overlap.

graph{((3y-17)/-2 - x)(- 4y + 16 - x)=0}

These lines overlap at $4 , 3$

$\textcolor{b l u e}{\therefore x = 4 , y = 3}$

To prove this, we can substitute the pronumerlas for their numeric value.

–2x – 3y = –17 , $x + 4 y = 16$

–2 xx 4 – 3 xx 3 = –17 ,  $4 + 4 \times 3 = 16$

–8 – 9 = –17 ,  $4 + 12 = 16$

-17 = –17 ,  $16 = 16$