Answer: x = 3, y = 1, z = 2
Step-by-step explanation:
EQ 1: x - y - z = 0
EQ 3: -x + 2y + z = 1
y = 1
EQ 2: 2x - 3y + 2z = 7 → 1(2x - 3y + 2z = 7) → 2x - 3y + 2z = 7
EQ 3: -x + 2y + z = 1 → -2( -x + 2y + z = 1) → -2x + 4y + 2z = 2
y + 4z = 9
y = 1 ⇒ 1 + 4z = 9
4z = 8
z = 2
Input y = 1 and z = 2 into one of the equations to solve for x:
EQ 1: x - y - z = 0
x - (1) - (2) = 0
x - 3 = 0
x = 3
Check:
EQ 2: 2x - 3y + 2z = 7
2(3) - 3(1) + 2(2) = 7
6 - 3 + 4 = 7
3 + 4 = 7
7 = 7 [tex]\checkmark[/tex]
