Question

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.

4x - y + 3z    =   12
x + 4y + 6z    = -32
5x + 3y + 9z    =   20

Answer 1

Note that adding the first two equations gives

`(4x-y+3z)+(x+4y+6z)=12+(-32)\implies5x+3y+9z=-20`

But the third equation says
`5x+3y+9z=20`, so there is no solution.