Question

Solve the following system of equations.

Variables x,y,z.

7x-y+z=-22
3x+2y-3z=-27
x-3y+2z=11

Answer 1

7x - y + z = -22 --->(2)
3x + 2y - 3z = -27
----------------
14x - 2y + 2z = -44 (result of multiplying by 2)
3x + 2y - 3z = -27
-----------------add
17x - z = -71

3x + 2y - 3z = -27 --->(3)
x - 3y + 2z = 11--->(2)
--------------------
9x + 6y - 9z = - 81 (result of multiplying by 3)
2x - 6y + 4z = 22 (result of multiplying by 2)
-------------------add
11x - 5z = - 59

17x - z = -71 --->(-5)
11x - 5z = -59
----------------
-85x + 5z = 355 (result of multiplying by -5)
11x - 5z = -59
---------------add
-74x = 296
x = - 296/74
x = - 4

17x - z = -71
17(-4) - z = -71
-68 - z = -71
-z = -71 + 68
-z = -3
z = 3

x - 3y + 2z = 11
-4 - 3y + 2(3) = 11
-4 - 3y + 6 = 11
-3y + 2 = 11
-3y = 11 - 2
-3y = 9
y = -3

check...
7x - y + z = -22
7(-4) - (-3) + 3 = -22
-28 + 3 + 3 = -22
-28 + 6 = -22
-22 = -22 (correct)

x = -4, y = -3, and z = 3