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)

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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)

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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)

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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.