Question

Solve using elimination 3 x + 2 y = -8 -x-2y=4

Answer 1

We have to solve this system of equations by elimination.

To do that, we substract (or add) one equation from the other in order to clear the value of one of the unknowns. In general, we have to multiply by a coefficient to cancel one of the unknowns.

In this case, if we add both equations, we get rid of "y" and can calculate the value of x:

`\begin{gathered} 3x+2y=-8 \\ -x-2y=4 \\ \Rightarrow(3x+2y)+(-x-2y)=-8+4 \\ 3x-x+2y-2y=-4 \\ 2x+0y=-4 \\ x=-(4)/(2) \\ x=-2 \end{gathered}`

With the value of x, we can solve for y:

`\begin{gathered} -x-2y=4 \\ -(-2)-2y=4 \\ 2-2y=4 \\ 2-4=2y \\ -2=2y \\ y=-(2)/(2) \\ y=-1 \end{gathered}`

Answer: The solution is x=-2 and y=-1.