Answer:
The solution of the system of equations be:
[tex]x=8,\:y=4[/tex]
Hence, option C is true.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}4x+7y=60\\ -4x+7y=-4\end{bmatrix}[/tex]
adding both the equations
[tex]-4x+7y=-4[/tex]
[tex]+[/tex]
[tex]\underline{4x+7y=60}[/tex]
[tex]14y=56[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}4x+7y=60\\ 14y=56\end{bmatrix}[/tex]
solve 14y for y
[tex]14y=56[/tex]
Divide both sides by 14
[tex]\frac{14y}{14}=\frac{56}{14}[/tex]
Simplify
[tex]y=4[/tex]
[tex]\mathrm{For\:}4x+7y=60\mathrm{\:plug\:in\:}y=4[/tex]
[tex]4x+7\cdot \:4=60[/tex]
[tex]4x+28=60[/tex]
Subtract 28 from both sides
[tex]4x+28-28=60-28[/tex]
Simplify
[tex]4x=32[/tex]
Divide both sides by 4
[tex]\frac{4x}{4}=\frac{32}{4}[/tex]
[tex]x=8[/tex]
Therefore, the solution of the system of equations be:
[tex]x=8,\:y=4[/tex]
Hence, option C is true.
