Answer:
The solution to the system of equations will be:
[tex]x=9,\:y=6[/tex]
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}2x-9y=-36\\ -14x+18y=-18\end{bmatrix}[/tex]
Multiply 2x-9y=-36 by 7
[tex]14x-63y=-252[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}14x-63y=-252\\ -14x+18y=-18\end{bmatrix}[/tex]
Adding both equations
[tex]-14x+18y=-18[/tex]
[tex]+[/tex]
[tex]\underline{14x-63y=-252}[/tex]
[tex]-45y=-270[/tex]
solve -45y = -270 for y
[tex]-45y=-270[/tex]
divide both sides by -45
[tex]\frac{-45y}{-45}=\frac{-270}{-45}[/tex]
Simplify
[tex]y=6[/tex]
For 14x-63y = -270 plug in y = 6
[tex]14x-63\cdot \:6=-252[/tex]
[tex]14x-378=-252[/tex]
Add 378 to both sides
[tex]14x-378+378=-252+378[/tex]
Simplify
[tex]14x=126[/tex]
Divide both sides by 14
[tex]\frac{14x}{14}=\frac{126}{14}[/tex]
Simplify
[tex]x=9[/tex]
Therefore, the solution to the system of equations will be:
[tex]x=9,\:y=6[/tex]
