Question

Homework: 5.1 Systems of Linear Equations

Answer 1

Answer:

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

$x=8,\:y=5$

Step-by-step explanation:

Given the system of linear equations

$7x-y=51$

$x+3y=23$

solving by the elimination method

$\begin{bmatrix}7x-y=51\\ x+3y=23\end{bmatrix}$

$\mathrm{Multiply\:}x+3y=23\mathrm{\:by\:}7\:\mathrm{:}\:\quad \:7x+21y=161$

$\begin{bmatrix}7x-y=51\\ 7x+21y=161\end{bmatrix}$

$7x+21y=161$

$-$

$\underline{7x-y=51}$

$22y=110$

so

$\begin{bmatrix}7x-y=51\\ 22y=110\end{bmatrix}$

now solving for y

$22y=110$

$\mathrm{Divide\:both\:sides\:by\:}22$

$\frac{22y}{22}=\frac{110}{22}$

$y=5$

$\mathrm{For\:}7x-y=51\mathrm{\:plug\:in\:}y=5$

$7x-y=51$

$7x-5=5$

$7x=56$

$\mathrm{Divide\:both\:sides\:by\:}7$

$\frac{7x}{7}=\frac{56}{7}$

$x=8$

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

$x=8,\:y=5$