Answer:
x = -5, y = 4, z = 3
Step-by-step explanation:
(1) 3x + y + 3z = -2
(2) 6x + 2y + 9z = 5
(3) -2x - y - z = 3
Step 1. Eliminate one of the variables in two of the equations
6x + 2y + 9z = 5 Subtract twice Equation (1)
6x + 2y + 6z = -4 from Equation (2)
3z = 9
z = 3
Step 2. Set up two new equations in two variables
3x + y + 9 = -2 Substitute z
-2x - y - 3 = 3 into (1) and (3)
(4) 3x + y = -11 Add Equations
(5) -2x - y = 6 (4) and (5)
x = -5
Step 3. Substitute x and z into one of the original equations
Substitute into (3)
-2(-5) - y - 3 = 3
10 - y - 3 = 3
7 - y = 3
- y = -4
y = 4
The solutions are x = -5, y = 4, z = 3.
Check:
(1) 3(-5) + 4 + 3(3) = -2
-15 + 4 + 9 = -2
-2 = -2
(2) 6(-5) + 2(4) + 9(3) = 5
-30 + 8 + 27 = 5
5 = 5
(3) -2(-5) - 4 - 3 = 3
10 - 4 - 3 = 3
3 = 3
