Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=0,\:x=6[/tex]
Step-by-step explanation:
Considering the system of the equations
[tex]\begin{bmatrix}2x-7y=12\\ -x+15y=-6\end{bmatrix}[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x-7y=12[/tex]
[tex]2x-7y+7y=12+7y[/tex]
[tex]2x=12+7y[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{12}{2}+\frac{7y}{2}[/tex]
[tex]x=\frac{12+7y}{2}[/tex]
[tex]\mathrm{Subsititute\:}x=\frac{12+7y}{2}[/tex]
[tex]\begin{bmatrix}-\frac{12+7y}{2}+15y=-6\end{bmatrix}[/tex]
[tex]-\frac{12+7y}{2}+15y=-6[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}2[/tex]
[tex]-\frac{12+7y}{2}\cdot \:2+15y\cdot \:2=-6\cdot \:2[/tex]
[tex]-\left(12+7y\right)+30y=-12[/tex]
[tex]-12+23y=-12[/tex]
[tex]-12+23y+12=-12+12[/tex]
[tex]23y=0[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}23[/tex]
[tex]\frac{23y}{23}=\frac{0}{23}[/tex]
[tex]y=0[/tex]
[tex]\mathrm{For\:}x=\frac{12+7y}{2}[/tex]
[tex]\mathrm{Subsititute\:}y=0[/tex]
[tex]x=\frac{12+7\cdot \:0}{2}[/tex]
[tex]x=\frac{12}{2}[/tex]
[tex]x=6[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=0,\:x=6[/tex]
