Final answer:
To solve the system algebraically, use the method of elimination or substitution. In this case, I'll use the elimination method. Multiply equations to eliminate terms, add equations to eliminate another term, substitute values to solve for one variable, andsolve the resulting system to find the values of the other variables. The solution to the system is x = -18, y = 26, z = 8.
Step-by-step explanation:
To solve the system algebraically, we can use the method of elimination or substitution. I will use the method of elimination.
Step 1: Multiply the first equation by 3 and the second equation by 2 to eliminate the y term:
-3x + 15y - 15z = -12
4x - 6y + 12z = -6
Step 2: Add the two equations to eliminate the x term:
x - z = -18
Step 3: Substitute the value of x into one of the original equations to solve for y:
4(-18) - 6y + 12z = -6
-72 - 6y + 12z = -6
- 6y + 12z = 66
Step 4: Solve the resulting system of equations to find the values of y and z:
- 6y + 12z = 66
y - z = -18
Using either substitution or elimination, we find y = 26 and z = 8.
Therefore, the solution to the system is x = -18, y = 26, z = 8.