Question

SOLVING EACH SYSTEM BY ELIMINATION


x+3y=5 x=-6y+14


HELP

Answer 1

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

`x=-4,\:y=3`

Explanation:

Given the system of the equations

`x+3y=5;\:x=-6y+14`

solving by elimination method

`\begin{bmatrix}x+3y=5\\ x=-6y+14\end{bmatrix}`

`\mathrm{Arrange\:equation\:variables\:for\:elimination}`

`\begin{bmatrix}x+3y=5\\ x+6y=14\end{bmatrix}`

`x+6y=14`

`-`

`\underline{x+3y=5}`

`3y=9`

`\begin{bmatrix}x+3y=5\\ 3y=9\end{bmatrix}`

solve
`3y=9` for
`y`:

`3y=9`

`(3y)/(3)=(9)/(3)`

`y=3`

`\mathrm{For\:}x+3y=5\mathrm{\:plug\:in\:}y=3`

Solve
`x+3\cdot \:3=5` for x:

`x+3\cdot \:3=5`

`x+9=5`

`x=-4`

Therefore,

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

`x=-4,\:y=3`