Respuesta :
Answer:
[tex]\begin{gathered} x=-2 \\ y=0 \end{gathered}[/tex]Step-by-step explanation:
Given the system of equations:
[tex]\begin{cases}-x+y=2 \\ 2x+y=-4\end{cases}[/tex]We'll multiply the first equation by 2:
[tex]\begin{cases}-x+y=2 \\ 2x+y=-4\end{cases}\rightarrow\begin{cases}-2x+2y=4 \\ 2x+y=-4\end{cases}[/tex]Then, we'll add up both equations and solve for y, as following:
[tex]\begin{cases}-2x+2y=4 \\ 2x+y=-4\end{cases}\rightarrow3y=0\rightarrow y=0[/tex]Now, we'll plug in this y-value in the second equation and solve for x, as following:
[tex]\begin{gathered} 2x+y=-4 \\ \rightarrow2x+0=-4 \\ \rightarrow2x=-4 \\ \\ \Rightarrow x=-2 \end{gathered}[/tex]This way, we'll have that the solution to the system of linear equations is:
[tex]\begin{gathered} x=-2 \\ y=0 \end{gathered}[/tex]