Question

-5x-18y=-28 and -10x+9y=-11 solve elimination

Answer 1

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

`x=2,\:y=1`

Explanation:

Given the equations

`-5x-18y=-28`

`-10x+9y=-11`

solving the system of the equation by elimination method

`\begin{bmatrix}-5x-18y=-28\\ -10x+9y=-11\end{bmatrix}`

`\mathrm{Multiply\:}-5x-18y=-28\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-10x-36y=-56`

`\begin{bmatrix}-10x-36y=-56\\ -10x+9y=-11\end{bmatrix}`

`-10x+9y=-11`

`-`

`\underline{-10x-36y=-56}`

`45y=45`

`\begin{bmatrix}-10x-36y=-56\\ 45y=45\end{bmatrix}`

solve 45y=5 for y:

`45y=45`

`(45y)/(45)=(45)/(45)`

`y=1`

`\mathrm{For\:}-10x-36y=-56\mathrm{\:plug\:in\:}y=1`

solve
`-10x-36\cdot \:1=-56` for x:

`-10x-36\cdot \:1=-56`

`-10x-36=-56`

Add 36 to both sides

`-10x-36+36=-56+36`

`-10x=-20`

`(-10x)/(-10)=(-20)/(-10)`

`x=2`

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

• 
  `x=2,\:y=1`