Question

find the solution of this system of equations5x+2y=-5-2x-2y=-16

Answer 1

We have to solve this system of equations:

$\begin{gathered} 5x+2y=-5 \\ -2x-2y=-16​ \end{gathered}$

The most appropiate way in this case is to add both equations and clear y.

Then solve for x:

$\begin{gathered} (5x+2y)+(-2x-2y)=(-5)+(-16) \\ 5x-2x+2y-2y=-5-16 \\ 3x+0y=-21 \\ x=-\frac{21}{3} \\ x=-7 \end{gathered}$

Then, we use any of the two equations to solve for y:

$\begin{gathered} -2x-2y=-16 \\ -2(-7)-2y=-16 \\ 14-2y=-16 \\ -2y=-16-14 \\ -2y=-30 \\ y=\frac{-30}{-2} \\ y=15 \end{gathered}$

Answer: x=-7 and y=15