Question

5x−4y=34
−x+8y=22
elimination

Answer 1

The solution to the system of equations is:

`x=10,\:y=4`

Explanation:

Given the system of equations

`\begin{bmatrix}5x-4y=34\\ -x+8y=22\end{bmatrix}`

Multiply -x+8y=22 by 5: -5x+40y=110

`\begin{bmatrix}5x-4y=34\\ -5x+40y=110\end{bmatrix}`

so adding the equations

`-5x+40y=110`

`+`

`\underline{5x-4y=34}`

`36y=144`

solve 36y = 144 for y:

`36y=144`

divide both sides by 36

`(36y)/(36)=(144)/(36)`

Simplify

`y=4`

For 5x-4y=34 plug in y=4

`5x-4\cdot \:4=34`

`5x-16=34`

Add 16 to both sides

`5x-16+16=34+16`

Simplify

`5x=50`

Divide both sides by 5

`(5x)/(5)=(50)/(5)`

Simplify

`x=10`

Therefore, the solution to the system of equations is:

`x=10,\:y=4`