Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=-\frac{12}{5},\:x=\frac{1}{5}[/tex]
Step-by-step explanation:
Given the equations
[tex]y=-32x+4;\:y=23x-7[/tex]
solving the system of the equations
[tex]\begin{bmatrix}y=-32x+4\\ y=23x-7\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y+32x=4\\ y-23x=-7\end{bmatrix}[/tex]
[tex]y-23x=-7[/tex]
[tex]-[/tex]
[tex]\underline{y+32x=4}[/tex]
[tex]-55x=-11[/tex]
[tex]\begin{bmatrix}y+32x=4\\ -55x=-11\end{bmatrix}[/tex]
[tex]-55x=-11[/tex]
[tex]\frac{-55x}{-55}=\frac{-11}{-55}[/tex]
[tex]x=\frac{1}{5}[/tex]
[tex]\mathrm{For\:}y+32x=4\mathrm{\:plug\:in\:}x=\frac{1}{5}[/tex]
[tex]y+32\cdot \frac{1}{5}=4[/tex]
[tex]\mathrm{Subtract\:}32\frac{1}{5}\mathrm{\:from\:both\:sides}[/tex]
[tex]y+32\cdot \frac{1}{5}-32\cdot \frac{1}{5}=4-32\cdot \frac{1}{5}[/tex]
[tex]y=-\frac{12}{5}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=-\frac{12}{5},\:x=\frac{1}{5}[/tex]
