Question

I just need help with this problem. I just don't know where to begin.

Given the system:

2x-3y+4z=21
5x+6y+8z=10
Z=x+y

What is the value of x?

Answer 1

move the x and y over to the left side on the bottom equation giving

z - x - y = 0

Answer 2

or in a better order

-x - y + z = 0

Answer 3

What should I do from there.

Answer 4

lets call each equation R1, R2, R3 so we have

2x-3y+4z=21 R1
5x+6y+8z=10 R2
- x - y + z = 0 R3

we need to get to a situation where we have an equation with one variable

Answer 5

multiply R1 by 5/2, and then subtract R1 - R2 = R2a

so you obtain a new formula R2a with only two variables y and z.

Answer 6

then you need to multiply R1 by somthing so you can subtract R1 - R3 = R3a

R3a being a new formula again with only y and z.

Answer 7

then you multiply R3a by something in order that you can cancel the y's when you do
R3a - R2a = R3b

you should be left with an equation with one variable which you can solve

Answer 8

and then plug that value back into R3a or R2a which have two variables, solve that. And then plug both the y value and z into R1 to find x

Answer 9

This process is called gaussian elimination

Answer 10

Alright bin working in a similar question like this for my exam review and I think I just got stumped but If I have any more questions ill post on this

Answer 11

kk

Answer 12

Than you for your help

Answer 13

np