Question

Solve the 3-variable systems of equations.
8x - 6y + 2z = -20
-3x + 6y - 15z = 51
2x + y + 3z = 0
The answers are x = 1, y = 4 and z = -2 according to my friend but can someone please help me find out how to get these answers using the elimination method? I need to show my work in order to recieve full credit. Will mark as Brainliest if it's correct!​

Answer 1

Answer: x = 1, y = 4, z = -2

Step-by-step explanation:

First, solve the third equation by the method of substitution for variable y.

2x + y + 3z = 0 -> y = -2x - 3z

Then, plug in y = -2x - 3z into the first equation of the system.

8x - 6y + 2z = -20

8x - 6 * (-2x - 3z) + 2z = -20

8x + 12x + 18z + 2z = -20

20x + 20z = -20

Repeat for the second equation.

-3x + 6y - 15z = 51

-3x + 6 * (-2x - 3z) -15z = 51

-3x - 12x - 18z - 15z = 51

-15x - 33z = 51

I have chosen to solve the equation  20x + 20z = -20 for z.

20z = -20x - 20

Divide both sides by 20.

z = -x - 1

Plug in z = -x - 1 into the equation -15x - 33z = 51 from an earlier step to find x.

-15x - 33 * (-x - 1) = 51

-15x + 33x + 33 = 51

18x = 51 - 33

x = 1

Now we have that:

x = 1

y = -2x - 3z

z = -x - 1

Plug in your value of x into the equation z = -x -1 to find z.

z = -1 - 1

z = -2

Plug in both your values of x and z into the equation y = -2x - 3z to find y.

y = -2 * 1 - 3 * (-2)

y = -2 + 6

y = 4