Solve the linear system of equations using the linear combination method.{4x−9y=202x−6y=16Enter your answers in the boxes.x = y =

The correct answer is:
x = -4; y = -4
Explanation:
We are going to eliminate the variable x. In order to do this, we are going to make the coefficients the same by multiplying the second equation by 2:
[tex] \left \{ {{4x-9y=20} \atop {2x-6y=16}} \right.
\\
\\\left \{ {{4x-9y=20} \atop {2(2x-6y=16)}} \right.
\\
\\\left \{ {{4x-9y=20} \atop {4x-12y=32}} \right. [/tex]
In order to eliminate x, we must subtract the transformed second equation from the first:[tex] \left \{ {{4x-9y=20} \atop {-(4x-12y=32)}} \right.
\\
\\-9y--12y=20-32
\\
\\-9y+12y=-12
\\
\\3y=-12 [/tex]
Divide both sides by 3:3y/3 = -12/3y = -4
Substitute this into the first equation:4x-9y = 204x-9(-4) = 204x--36 = 204x+36 = 20
Subtract 36 from each side:4x+36-36 = 20-364x = -16
Divide both sides by 4:4x/4 = -16/4x = -4