## alyannahere 3 years ago solve the system x - 2y + z =4 -x + 4y - 3z =2 2x + y + 10z=10

1. rshextall

What math are you in because you can either put this in a matrix which is faster or you can write it all out by hand

2. Monkeyball

Do you know matrices?

3. alyannahere

nope. i think it has to be the traditional way

4. rshextall

Then you need to solve for each variable one at a time. Do you need help getting started?

5. alyannahere

6. rshextall

7. rshextall

Just add 2y and subtract z from both sides of the equation \[x-2y+2y+z-z=4+2y-z\] \[x=4+2y-z\]

8. rshextall

Do you see what happened there?

9. alyannahere

yup !

10. rshextall

Then you need to plug it into one of the other equations and solve for either y or z

11. alyannahere

so plugging it into the 2nd equation mates it 2y-2z=6 ? then?

12. rshextall

Right!!!

13. rshextall

It takes a while but it's not to difficult, but its easy to make simple mistakes like forgetting a minus sign and stuff

14. alyannahere

then?

15. rshextall

Then solve for either y or z

16. rshextall

Then you have to both x and the other into the last equation and solve for the last variable

17. rshextall

You can check your answer by plugging your answers for x, y, and z into the first equations. They should work for all 3 equations

18. rshextall

Did you get it?

19. alyannahere

z=-1 y=2 x=9. yup i got it thanks!

20. alyannahere

@rshextall but can you show me how to do the matrix, it's in the next lesson of the book so i think i should learn it too.

21. rshextall

You have to learn the rules of matrices. They're a bit more in depth than we can really get into on here. If you like I can help you with your homework with it when you get it