Question

Solve the 3-variable systems of equations.
-x + 2y + 2z = -4
4x + y - 3z = 13
x - 5y + z = -23
The answers are x = -2, y = 3 and z = -6 according to my friend but can someone help me solve the problem using elimination? I need to show my work in order to recieve full credit. Will mark as Brainliest if it's correct!​

Answer 1

Answer:

x = -2, y = 3, z = -6

Step-by-step explanation:

First, solve the third equation by substitution for variable z.

x - 5y + z = -23 -> z = -x + 5y - 23

In the first equation, plug the variable z in.

-x + 2y + 2z = -4

-x + 2y + 2 * (-x + 5y - 23) = -4

-x + 2y - 2x + 10y - 46 = -4

-3x + 12y = -4 + 46

-3x + 12y = 42

Do the same for the second equation.

4x + y - 3z = 13

4x + y - 3 * (-x + 5y - 23) = 13

4x + y + 3x - 15y + 69 = 13

7x - 14y = -56

Solve 7x - 14y = -56 for x.

Divide by 7 on both sides: x - 2y = -8

Express in terms of x: x = 2y - 8

Plug in x = 2y - 8 in the equation -3x + 12y = 42 to find y.

-3 * (2y - 8) + 12y = 42

-6y + 24 + 12y = 42

6y = 42 - 24

y = 3

Substitute your value of y into x = 2y - 8.

x = 2y - 8

x = 6 - 8

x = -2

We already substituted for variable z earlier, let's plug the values of x and y into the expression z = -x + 5y - 23 to find z.

z = -x + 5y - 23

z = 2 + 15 - 23

z = -6