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

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`-x+y=4`

`2x-4y=-34`

Write the system of equations as an augmented matrix.

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

Multiply the first line by a 2.

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

Eliminate the first column.

`[[-2,2|8],[0,-2|-26]]`

 

`-2y=-26`

`y=13`

 

`-x+y=4`

`-x+13=4`

`x=9`

 

The solution set is (9, 13).

 

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