Question

What is the solution to the system?

{2x+y−z=−3
{5x−2y+2z=24
{3x−z=5


a. (-5, 4, -3)
b. (4, 1, 8)
c. (2, −6, 1)
d. (−1, 0, −8)

Answer 1

2x + y - z = -3 .....multiply by 2
5x - 2y + 2z = 24
-----------------
4x + 2y - 2z = -6 (result of multiplying by 2)
5x - 2y + 2z = 24
----------------add
9x = 18
x = 18/9
x = 2

3x - z = 5
3(2) - z = 5
6 - z = 5
6 - 5 = z
1 = z

2x + y - z = -3
2(2) + y - 1 = -3
4 + y - 1 = -3
y + 3 = -3
y = -3 - 3
y = -6

solution is : (2.-6,1)