Answer:
Substitute the 2nd and 3rd equations for x and y into the first equation.
Use the distributive property to simplify terms
Combine like terms to get 12z = -24
Solve for z = -2
Solve for x and Y by substituting z into 2nd and 3rd equations
Step-by-step explanation:
2x - y + 3z = -12
x = 3 + 2z
y = -6 - 5z
Substitute;
2(3 + 2z) - (-6 - 5z) + 3z = -12
Distribute;
6 + 4z + 6 + 5z + 3z = -12
Combine like terms;
12 + 12z = -12
Subtract 12 from both sides;
12z = -24
Divide by 12 to get z;
z = -2
Substitute z into x and y to get their values;
x = 3 + 2(-2)
x = 3 - 4
x = -1
y = -6 - 5(-2)
y = -6 + 10
y = 4
Now to check;
2x - y + 3z = -12
2(-1) - (4) + 3(-2) = -12
-2 - 4 - 6 = -12
-12 = -12
CORRECT!
