Solve the system of equation.
x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8
x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8
First thing to check is that we have three equations and three unknowns, which is fine. If there are more unknowns than equations then there is a problem with the question.
x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8
we need to eliminate one unknown by combining pairs of equations. Lets say we remove the y terms.
x- 2y+ 3z = 5
3x + y = -5 (multiply by 2)
x- 2y+ 3z = 5
6x + 2y = -10
Add these two and y terms are removed.
7x+3z=-5
Do the same with, but this time subtract the two and the y terms are removed
3x + y = -5
-2x+y + z = 8
5x-z=-13
We now have two equations and two unknwons
7x+3z=-5
5x-z=-13 (multiply by 3)
7x+3z=-5
15x-3z=-39
and add
22x=-44, so x=-2
substitute in here to find y
3x + y = -5
the substitute in one of the above to find z