Find the ordered pair (x,y) that satisfies the system of equations
\(\begin{align*} 2x + y &=-7,\\ x &=4+2y. \end{align*}\)
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!