Question

x-2y+3z=18
9x+2y-z=-2
-6x-y+2z=4
I need to solve the system for x,y,z

Answer 1

A) x-2y+3z=18
B) 9x+2y-z=-2
C) -6x-y+2z=4

A) -2y = -x -3z +18
B) 2y = -9x +z -2
Adding these 2 equations yields equation D
D) -10x -2z +16 = 0

B) 9x+2y-z=-2
C) -6x-y+2z=4 Multiplying this equation 2 yields
C2) -12x -2y + 4z = 8

Adding these equations together
B) 9x+2y-z=-2
C2) -12x -2y + 4z = 8 produces

E) -3x + 3z = 6 then we multiply equation D) by 1.5 producing
D2) -15x -3z = -24

Adding these 2 together produces
-18x = -18
x = 1

That should be a good start for you.

Answer 2

x - 2y + 3z = 18
9x + 2y - z = -2
--------------add
10x + 2z = 16

9x + 2y - z = -2
-6x - y + 2z = 4 -->(2)
---------------
9x + 2y - z = -2
-12x - 2y + 4z = 8 (result of multiplying by 2)
----------------add
-3x + 3z = 6

10x + 2z = 16 -->(-3)
-3x + 3z = 6 --> (2)
----------------
-30x - 6z = - 48 (result of multiplying by -3)
-6x + 6z = 12 (result of multiplying by 2)
----------------add
-36x = - 36
x = 1

now sub 1 in for x
-3x + 3z = 6
-3(1) + 3z = 6
-3 + 3z = 6
3z = 6 + 3
3x = 9
z = 3

now sub 1 in for x and 3 in for y in any of the original equations
x - 2y + 3z = 18
1 - 2y + 3(3) = 18
1 - 2y + 9 = 18
-2y + 10 = 18
-2y = 18 - 10
-2y = 8
y = -4

check by subbing in known values
9x + 2y - z = -2
9(1) + 2(-4) - 3 = -2
9 - 8 - 3 = -2
9 - 11 = -2
-2 = -2 (correct)

x = 1, y = -4, z = 3 or (1,-4,3)