Question

Solve the system of the equation by elimination method. 5x+2y=-37 4x+y=-29eliminating the y variable.

Answer 1

To eliminate the y variable we multiply the second equation by -2, then we have:

$\begin{gathered} 5x+2y=-37 \\ -8x-2y=58 \end{gathered}$

now we add the equations:

$\begin{gathered} -3x=21 \\ x=\frac{21}{-3} \\ x=-7 \end{gathered}$

Once we have x we can find y by plugging the value of x into the first equation and solve for y:

$\begin{gathered} 5(-7)+2y=-37 \\ -35+2y=-37 \\ 2y=35-37 \\ y=-\frac{2}{2} \\ y=-1 \end{gathered}$

Then the solution is x=-7 and y=-1.