5-step procedure to solve by elimination: x - y - 2z = 4, -x + 2y + z = 1, and -x + y - 3z = 11. Write your answer as a point, an ordered triple: (x,y,z)

Question

I need help!!!PLZ!!!!!!!!!!!

 x - y - 2z = 4  They are three different equations, but one answer

-x + 2y + z = 1

 -x + y - 3z = 11

Answer 1

We have three equations and three unknowns.

Find the values for x, y, and z we are going to use all three equations in an elimination and substitution process to solve for x, y, and z.

First, we will use equations one and two and add them together to eliminate the x variable and get

y - z = 5

Then we will add equations one and three together to eliminate variables x and y to solve for z

-5z = 15

z = -3

no substitute z equals -3 into equations one and two result from above to solve for y

y - -3 = 5

y + 3 = 5

y=2

No substitute y = 2 and z = - 3 into equation one to solve for X

x - 2 - 2(-3) =4

x-2+6=4

x + 4 =4

so x=0

Final answer is (0,2,-3)

Now we’ll do a couple double checks in equation to an equation 3 to verify that these answers are correct

Equation two

0+2(2)+(-3)=1. Checks

Equation 3

0+2-3(-3) =11 checks

A few summary tips

You need to use all the equations in solving for the variables. If you don’t use all the equations you’re gonna end up with an incorrect answer. Bottom line is your eliminating equations in different combinations to solve for the unknown variables and then back substituting them in to solve for the variables and then in the end when you think you have an answer, substitute them into one of the original equations to make sure it checks out