Question

What is the solution to the system of equations? {2x-2y+z=5 2x-2y+3z=7 -3x-3y+3z=9

Answer 1

2x - 2y + z = 5....multiply by -1
2x - 2y + 3z = 7
-------------------
-2x + 2y - z = -5 (result of multiplying by -1)
2x - 2y + 3z = 7
-------------------add
2z = 2
z = 2/2 = 1

2x - 2y + z = 5.....multiply by 3
-3x - 3y + 3z = 9...multiply by 2
-------------------
6x - 6y + 3z = 15 (result of multiplying by 3)
-6x - 6y + 6z = 18 (result of multiplying by 2)
-------------------add
-12y + 9z = 33

-12y + 9(1) = 33
-12y + 9 = 33
-12y = 33 - 9
-12y = 24
y = -24/12
y = -2

2x - 2y + z = 5
2x - 2(-2) + 1 = 5
2x + 4 + 1 = 5
2x + 5 = 5
2x = 5 - 5
2x = 0
x = 0

solution is : (0,-2,1)