`-x + y = 4, 2x - 4y = -34` Use matricies to solve the system of equations. Use Gaussian elimination with back-substitution.

Rewrite in matrix form

`[[-1, 1, | 4], [2, -4 | ,-34]]`

Divide the first row by -1` `

`[[1,-1,|4],[2,-4,|-34]]`

Multiply the first row by 2

`[[2,-2,|8], [2,-4,|-34]]`

Subtract the first row from the second row and restore it

`[[1,-1,|-4],[0,-2,|-26]]`

Divide the second row by -2
`[[1,-1,|-4], [0,1,|13]]`

Multiply the second row by -1

`[[1,-1,|-4],[0,-1,|-13]]`

Subtract the second row from the first row

`[[1,0,|9],[0,1,|13]]`

Therefore, `x = 9 and y = 13`