+0  
 
0
51
1
avatar

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
 #1
avatar
0

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

26 Online Users

avatar