Question

Use elimination to solve the system of equations. Enter your answer as an ordered triple; example: (2, -3, 4)

{4x + y + 3z = 0
2x - 2y - z = 10
3x - 2y + 2z = 11

Answer 1

We have the following system:
4x+y+3z=0
2x-2y-z=10
3x-2y+2z=11

so, we have the following matrix.
4 1 3 0
2 -2 -1 10
3 -2 2 11

We start:
4 1 3 0
0 -5 -5 20 2R₂-R₁
0 -11 -1 44 4R₃-3R₁


4 1 3 0
0 -5 -5 20
0 0 50 0 5R₃-11R₂

Then:
50Z=0 ⇒ Z=0/50=0

-5y-5Z=20
-5y-5(0)=20
-5y-0=20
-5y=20
y=-20/5
y=-4



4x+y+3z=0
4x-4+3(0)=0
4x-4=0
4x=4
x=4/4
x=1

Answer: (1,-4,0)