SOLUTION: Using the matrices find a general solution 2x-y+3z=5 -x+4y+4z=-1 if you could show how you did this I would really appreciate it. ty

Convert to this matrix:



We want to use row operations to get it looking like this: 

First we get the two zeros:

To get a 0 where the -1 is on the bottom left, multiply
the second row by 2



and add the first row to the 2nd row



To get a 0 where the remaining -1 is on the first row, multiply
the first row by 7



and add the second row to the first row:



Now we get the two 1's

Divide the first row through by 14, and the second row
through by 7



and reduce:



convert back to a system of equations:



or



Solution: choose any value k for z then annex z=k to the system:



or

(x,y,z) = (,,k)

Edwin