Answer:
(x, y) = (2, -7)
Explanation:
Given the system of equations:
[tex]\begin{cases}x+y=-5 \\ x-y=9\end{cases}[/tex]We are required to solve the system by the elimination method.
In order to do this, add the two equations.
[tex]\begin{gathered} \begin{cases}x+y=-5 \\ x-y=9\end{cases} \\ --------- \\ 2x=4 \end{gathered}[/tex]Divide both sides by 2 to solve for x.
[tex]\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]Next, substitute x=2 into any of the equations to solve for y.
Using the first equation:
[tex]\begin{gathered} x+y=-5 \\ 2+y=-5 \\ y=-5-2 \\ y=-7 \end{gathered}[/tex]The solution to the system of linear equations is (x, y) = (2, -7).
