# How do you solve 2x+y= -92 and 2x+2y= -98 using substitution?

Aug 3, 2016

$x = - 43 , y = - 6$

#### Explanation:

It is useful to notice that both the given equations have a $2 x$ term.

Make 2x" the subject of each equation:

$\textcolor{b l u e}{2 x = - y - 92} \text{ and } \textcolor{red}{2 x = - 2 y - 98}$

Obviously $\textcolor{b l u e}{2 x} = \textcolor{red}{2 x}$ but we can use this to form a new equation.

$\text{ if " color(blue)(2x) " " = " } \textcolor{red}{2 x}$

Then: $\text{ } \textcolor{b l u e}{- y - 92} = \textcolor{red}{- 2 y - 98}$

Solve for y:

$- y + 2 y = - 98 + 92$

$\text{ } y = - 6$

Now use $y = - 6$ to solve for $x$

$\textcolor{b l u e}{2 x = - \left(- 6\right) - 92}$

color(blue)(2x = 6-92) =-86

$x = - 43$