Question

Solve the system of equations.

\begin{aligned} &-6y+11x = -36 \\\\ &-4y+7x=-24 \end{aligned}
​

−6y+11x=−36
−4y+7x=−24
​

Answer 1

The solutions to the system of equations will be:

`y=6,\:x=0`

Explanation:

Given the equation

`-6y+11x=-36`

`-4y+7x=-24`

solving the system of equations

`\begin{bmatrix}-6y+11x=-36\\ -4y+7x=-24\end{bmatrix}`

`\mathrm{Multiply\:}-6y+11x=-36\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12y+22x=-72`

`\mathrm{Multiply\:}-4y+7x=-24\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:-12y+21x=-72`

`\begin{bmatrix}-12y+22x=-72\\ -12y+21x=-72\end{bmatrix}`

`-12y+21x=-72`

`-`

`\underline{-12y+22x=-72}`

`-x=0`

`\begin{bmatrix}-12y+22x=-72\\ -x=0\end{bmatrix}`

solving for x

`-x=0`

`\mathrm{Divide\:both\:sides\:by\:}-1`

`(-x)/(-1)=(0)/(-1)`

`x=0`

`\mathrm{For\:}-12y+22x=-72\mathrm{\:plug\:in\:}x=0`

`-12y+22\cdot \:0=-72`

`-12y+0=-72`

`-12y=-72`

`\mathrm{Divide\:both\:sides\:by\:}-12`

`(-12y)/(-12)=(-72)/(-12)`

`y=6`

Therefore, the solutions to the system of equations will be:

`y=6,\:x=0`