Question

System of linear equations:
x + 2y+6z= 4
-3x+2y-z= -4
4x+ 2z=16

Answer 1

Pick one variable to eliminate. Let us say we want to eliminate z.
Find z from the last equation in terms of x put it in the first 2 equations and you will have two equations and 2 unknowns, namely, x and y.
Now pick another variable to eliminate from these two equations and you would have solved for one variable. Then you can put back in the equations and find the other two.

Answer 2

So I can use the first two equations and eliminate z?

Answer 3

Yes. Find z from the third equation and substitute that for z in first 2 equations.

Answer 4

Am I supposed to get x by itself by eliminating y? or do i use substitution

Answer 5

Whichever method you find convenient. What are the 2 equations you are getting with x and Y?

Answer 6

After canceling out z using the first two equations...I got
x+2y=4
-18x+12y=-24

Answer 7

I need help, medal will be awarded, for this question and my question.
http://openstudy.com/study#/updates/529a99bfe4b0a454724fff80

Answer 8

After substituting z I am getting:
-x + 2y = 4
-11x + 2y = -44

Answer 9

You eliminated z by multiplying by 11?

Answer 10

4x + 2z = 16
2z = 16 - 4x
z = 8 - 2x

Answer 11

Ok I see where that is coming from. Now where do i plug in the equation we found for z?

Answer 12

z goes into the first and second equations.

Answer 13

so with x+2y+6(-2x+4)=4
What do I do to the y still left

Answer 14

simplify the above first. keep x and y on the left and take the constant to the right.

Answer 15

so on the first one -13x+2y=-20?

Answer 16

no. try again.

Answer 17

z = 8 - 2x
Make the correct substitution in first equation.

Answer 18

let me check my work

Answer 19

-11x+2y=-44?

Answer 20

See it here https://www.khanacademy.org/math/trigonometry/systems_eq_ineq/fancier_systems_precalc/v/systems-of-three-variables

Answer 21

yes. Now we have one equation with no z.
Sub z in equation 2.

Answer 22

for the second one : -x+2y=4?

Answer 23

yes. Now you can easily eliminate y from these two equations by subtracting.

Answer 24

I got x=4.8

Answer 25

yes. put that in the last equation, -x+2y=4, and solve for y.

Answer 26

Then put x in z = 8 - 2x and solve for z.

Answer 27

z=-1.6?

Answer 28

yes all three values are correct.

Answer 29

If you want to know whether you got the right answers you can always put the x,y,z values you got into each of the equations and see if it satisfies all three.

Answer 30

thank you so much for being patient! i just checked back and plugged in all the values in the equations and checked them. They are all correct!This was much appreciated

Answer 31

you are very welcome.