Question

Homework: 5.1 Systems of Linear Equations

core: 0 of 1 pt
1 of 9 (5 complete)
5.1.19
Solve by the elimination
method.
7x - y = 51
x + 3y = 23
The solution set is
(Simplify your answer. Type an ordered

Answer 1

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

`x=8,\:y=5`

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`

`(22y)/(22)=(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`

`(7x)/(7)=(56)/(7)`

`x=8`

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

`x=8,\:y=5`