Solve The System

Question

Solve the System. Give answer as (x,y,z).

−5x−4y+3z=15

−3x−8y−3z=5

−2x−16y+3z=24

(x,y,z)

Answer 1

eliminates Z....

equation 1 + equation 2:

-8x - 12y = 20

2x + 3y = -5

equation 2 + equation 3:

-5x - 24y = 29

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2 by 2 system:

2x + 3y = -5

-5x - 24y = 29

8*equation 1 + equation 2:

11x = -11

x = -1

2(-1) + 3y = -5

-2 + 3y = -5

3y = -3

y = -1

1st equation:

(-5)(-1) - 4(-1) + 3z = 15

5 + 4 + 3z = 15

9 + 3z = 15

3z = 6

z = 2

checks if (x=-1, y=-1,z=2) is the solution:

1st equation:

(-5)(-1) - 4(-1) + 3(2) =

5 +4+6=15

YES

2nd equation:

(-3)(-1) - 8(-1) -3(2)=

3 +8-6 = 5

YES

3rd equation:

(-2)(-1)-16(-1)+3(2) =

2+16+6 = 24

YES

The official solution is x=-1, y=-1, z=2