Question

Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2

I really need help..
1 1 1 -5
1 -1 3 -1
4 1 1 1 -2


I've done so many different methods to solve this and I get stuck..

Answer 1

agree with

1 1 1 -5
1 -1 3 -1
4 1 1 -2 -----> you had an extra 1 in there

1 1 1 -5
0 2 -2 -4 #1 - #2
0 3 3 -18

1 1 1 -5
0 1 -1 -2 #2 divided by 2
0 1 1 -6 #3 divided by 3

1 1 1 -5
0 1 -1 -2
0 0 -2 4 #2 - #3

1 1 1 -5
0 1 -1 -2
0 0 1 -2

from #3:
z = -2
in #2:
y - z = -2
y + 2 = -2
y = -4

in #1
x + y + z = -5
x - 4 - 2 = -5
x = 1

x = 1, y = -4, z = -2

Answer 2

thank you!