Final answer:
The system is solved by substitution by first inserting the given value of z into the other equations, simplifying, and solving for x and y sequentially. The final solution to the system of equations is x = -3, y = 3, and z = 5.
Step-by-step explanation:
To solve the system by substitution, we start by analyzing the given equations.
2x - y + z = -4
z = 5
-2x + 3y - z = 10
With the value of z given as 5, we substitute it into the first and third equations.
2x - y + 5 = -4
-2x + 3y - 5 = 10
After substitution, we simplify and solve for y in the first equation:
2x - y = -9
y = 2x + 9
Then, substitute y into the third equation:
-2x + 3(2x + 9) - 5 = 10
-2x + 6x + 27 - 5 = 10
4x + 22 = 10
4x = -12
x = -3
With x found, we substitute it back into the equation for y:
y = 2(-3) + 9
y = -6 + 9
y = 3
Now we have found that x = -3, y = 3, and z = 5.