Answer: x = 1, y = 1, z = 0
Step-by-step explanation:
EQ 1: -2x + 2y + 3z = 0 EQ 2: -2x - y + z = -3
EQ 3: 2x + 3y + 3z = 5 EQ 3: 2x + 3y + 3z = 5
5y + 6z = 5 2y + 4z = 2
Eliminate one of the variables for the new equations:
2(5y + 6z = 5) --> 10y + 12z = 10
-3(2y + 4z = 2) --> -6y - 12z = -6
4y = 4
y = 1
Substitute y = 1 into one of the new equations to solve for z:
5(1) + 6z = 5
5 + 6z = 5
6z = 0
z = 0
Substitute y = 1 and z = 0 into one of the original equations to solve for x:
2x + 3(1) + 3(0) = 5
2x + 3 + 0 = 5
2x = 2
x = 1
