Answer:
The value of x of the solution to the system of equations
Hence, option (C) is true.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x=2y-4\\ 7x+5y=-66\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}x-2y=-4\\ 7x+5y=-66\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}x-2y=-4\mathrm{\:by\:}7\:\mathrm{:}\:\quad \:7x-14y=-28[/tex]
[tex]\begin{bmatrix}7x-14y=-28\\ 7x+5y=-66\end{bmatrix}[/tex]
subtracting 7x-14y=-28 from 7x+5y=-66
[tex]7x+5y=-66[/tex]
[tex]-[/tex]
[tex]\underline{7x-14y=-28}[/tex]
[tex]19y=-38[/tex]
so the equations become
[tex]\begin{bmatrix}7x-14y=-28\\ 19y=-38\end{bmatrix}[/tex]
solve 19y = -38
[tex]19y=-38[/tex]
Divide both sides by 19
[tex]\frac{19y}{19}=\frac{-38}{19}[/tex]
[tex]y=-2[/tex]
[tex]\mathrm{For\:}7x-14y=-28\mathrm{\:plug\:in\:}y=-2[/tex]
[tex]7x-14\left(-2\right)=-28[/tex]
[tex]7x+28=-28[/tex]
[tex]7x=-56[/tex]
Divide both sides by 7
[tex]\frac{7x}{7}=\frac{-56}{7}[/tex]
[tex]x=-8[/tex]
Therefore, the value of x of the solution to the system of equations
Hence, option (C) is true.
