6x-6y-4z=-10
-5x+4y-z=-12
2x+3y-2z=9

6x-6y-4z=-10 -5x+4y-z=-12 2x+3y-2z=9

1)  6x - 6y - 4z = -10
2)  -5x + 4y - z = -12
3)  2x + 3y - 2z = 9

Multiply equation two by 4.
4 * (-5x + 4y - z) = -12 * 4
4)  -20x + 16y - 4z = -48

Subtract equation four from equation one.
6x -    6y - 4z = -10
-(-20x + 16y - 4z = -48)
-----------------------------
26x - 22y      = 38
5)  26x - 22y = 38

Multiply equation two by 2.
2 * (-5x + 4y - z) = -12 * 2
6)  -10x + 8y - 2z = -24

Subtract equation six from equation three.
2x + 3y - 2z =    9
-(-10x + 8y - 2z = -24)
----------------------------
12x - 5y      = 33
7)  12x - 5y = 33

Multiply equation five by 5.
5 * (26x - 22y) = 38 * 5
8)  130x - 110y = 190

Multiply equation seven by 22.
22 * (12x - 5y) = 33 * 22
9)  264x - 110y = 726

Subtract equation eight from equation nine.
264x - 110y = 726)
-(130x - 110y = 190)
--------------------------
134x        = 536
134x = 536
x = 4  <<<<<<<<<<<<<<<<<<<

Plug the value of x into equation seven.
12x - 5y = 33
12(4) - 5y = 33
48 - 5y = 33
-5y = -15
y = 3  <<<<<<<<<<<<<<<<<<<

Plug the values for x and y into equation two.
-5x + 4y - z = -12
-5(4) + 4(3) - z = -12
-20 + 12 - z = -12
-z = -12 + 20 - 12
-z = -4
z = 4  <<<<<<<<<<<<<<<<<<<

x = 4, y = 3, z = 4

Check the answers by plugging all three values
into the original equations.

One:
6x - 6y - 4z = -10
6(4) - 6(3) - 4(4) = -10
24 - 18 - 16 = -10
6 - 16 = -10
-10 = -10

Two:
-5x + 4y - z = -12
-5(4) + 4(3) - 4 = -12
-20 + 12 - 4 = -12
-8 - 4 = -12
-12 = -12

Three:
2x + 3y - 2z = 9
2(4) + 3(3) - 2(4) = 9
8 + 9 - 8 = 9
9 = 9

All values are correct.
by Level 11 User (78.4k points)