Question

-x+5y=8 3x+7y=-3 find the equation​

Answer 1

The solution to the system of equations be:

`x=-(71)/(22),\:y=(21)/(22)`

Explanation:

Given the system of equation

`\begin{bmatrix}-x+5y=8\\ 3x+7y=-3\end{bmatrix}`

Multiply -x+5y=8 by 3: -3x+15y=24

`\begin{bmatrix}-3x+15y=24\\ 3x+7y=-3\end{bmatrix}`

Add the equations

`3x+7y=-3`

`+`

`\underline{-3x+15y=24}`

`22y=21`

solving 22y=21 for y

`22y=21`

Divide both sides by 22

`(22y)/(22)=(21)/(22)`

Simplify

`y=(21)/(22)`

For -3x+15y=24 plug in y = 21/22

`-3x+15\cdot (21)/(22)=24`

Subtract 15 · 21/22 from both sides

`-3x+15\cdot (21)/(22)-15\cdot (21)/(22)=24-15\cdot (21)/(22)`

`-3x=(213)/(22)`

Divide both sides by -3

`(-3x)/(-3)=((213)/(22))/(-3)`

`x=-(71)/(22)`

The solution to the system of equations be:

`x=-(71)/(22),\:y=(21)/(22)`