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Find the solution for the system of linear equations-x + y = 2 and 2x + y = -4

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Answer:


\begin{gathered} x=-2 \\ y=0 \end{gathered}

Explanation:

Given the system of equations:


\begin{cases}-x+y=2 \\ 2x+y=-4\end{cases}

We'll multiply the first equation by 2:


\begin{cases}-x+y=2 \\ 2x+y=-4\end{cases}\rightarrow\begin{cases}-2x+2y=4 \\ 2x+y=-4\end{cases}

Then, we'll add up both equations and solve for y, as following:


\begin{cases}-2x+2y=4 \\ 2x+y=-4\end{cases}\rightarrow3y=0\rightarrow y=0

Now, we'll plug in this y-value in the second equation and solve for x, as following:


\begin{gathered} 2x+y=-4 \\ \rightarrow2x+0=-4 \\ \rightarrow2x=-4 \\ \\ \Rightarrow x=-2 \end{gathered}

This way, we'll have that the solution to the system of linear equations is:


\begin{gathered} x=-2 \\ y=0 \end{gathered}

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