Question

Y=−32x+4and y=23x−7

Answer 1

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=-\frac{12}{5},\:x=\frac{1}{5}$

Step-by-step explanation:

Given the equations

$y=-32x+4;\:y=23x-7$

solving the system of the equations

$\begin{bmatrix}y=-32x+4\\ y=23x-7\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}y+32x=4\\ y-23x=-7\end{bmatrix}$

$y-23x=-7$

$-$

$\underline{y+32x=4}$

$-55x=-11$

$\begin{bmatrix}y+32x=4\\ -55x=-11\end{bmatrix}$

$-55x=-11$

$\frac{-55x}{-55}=\frac{-11}{-55}$

$x=\frac{1}{5}$

$\mathrm{For\:}y+32x=4\mathrm{\:plug\:in\:}x=\frac{1}{5}$

$y+32\cdot \frac{1}{5}=4$

$\mathrm{Subtract\:}32\frac{1}{5}\mathrm{\:from\:both\:sides}$

$y+32\cdot \frac{1}{5}-32\cdot \frac{1}{5}=4-32\cdot \frac{1}{5}$

$y=-\frac{12}{5}$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=-\frac{12}{5},\:x=\frac{1}{5}$