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# help mee

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Find the ordered pair (x,y) that satisfies the system of equations

\begin{align*} 2x + y &=-7,\\ x &=4+2y. \end{align*}

Sep 24, 2022

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Hi Guest!

$$2x+y=-7 \hspace{0.65cm} (1) \\ x=4+2y \hspace{1.00cm} (2)\\$$

Multiply equation (2) by -2:

Thus, our system of equations becomes:

$$2x+y=-7 \\ -2x=-8-4y \\$$

Now, add the above two equations:

$$(2x-2x)+y=-7+(-8-4y) \\ \iff y=-15-4y \\ \iff 5y=-15 \\ y=-3$$

So, using either (2) or (1), we get (by (2)): $$x=4+2(-3)=4-6=-2$$

Therefore, $$(-2,-3)$$ is the solution to the system of the equations.
I hope this helps!

Sep 24, 2022