Step-by-step explanation:
x + 3y + 2z = 7
2x − y + z = 9
-x + 4y + 5z = 14
First add the first and third equations to eliminate x.
7y + 7z = 21
Simplify:
y + z = 3
Solve for y:
y = 3 − z
Substitute into the first two equations:
x + 3(3 − z) + 2z = 7
2x − (3 − z) + z = 9
Simplify:
x + 9 − 3z + 2z = 7 → x − z = -2
2x − 3 + z + z = 9 → 2x + 2z = 12 → x + z = 6
Add the equations to eliminate z.
2x = 4
x = 2
Therefore, z = 4 and y = -1.
