Question

Solve the system.
x - y + z = -1
x + y - 2z = 7
- 2x + 4y + 2z = - 4

Answer 1

To solve the given system of linear equations x - y + z = -1, x + y - 2z = 7, and -2x + 4y + 2z = -4, you can use the elimination method to find the values of x, y, and z.

Step-by-step explanation:

To solve the system of equations given below, we can use methods such as substitution, elimination, or matrix operations.

1. x - y + z = -1
2. x + y - 2z = 7
3. -2x + 4y + 2z = -4

Let's use the elimination method:

1. Add equation (1) and equation (2) to eliminate y:
2. x - y + z + x + y - 2z = -1 + 7
3. 2x - z = 6 ⇒ z = 2x - 6 (Equation 4)
4. Substitute z from equation (4) into equation (1):
5. x - y + 2x - 6 = -1
6. 3x - y = 5 ⇒ y = 3x - 5 (Equation 5)
7. Substitute y and z from equations (5) and (4) into equation (3):
8. -2x + 4(3x - 5) + 2(2x - 6) = -4
9. Solve for x, then use x's value to find y and z.

Following these steps will provide the solution to the system of equations. Each algebraic step should be checked for accuracy before proceeding to the next.