Question

I need help working this out!
Question:
Solve the following system of equations.
x+y-4z=-7
2x+3y-3z=-6
2x+2y-z=0

I know that my first step is adding two equations together to get x by it's self.
So I took 2x+3y-3z=-6 and multiplied it by -1. So that I could add it to 2x+2y-z=0, and get the x by it's self. Now if that was right I got x-1y+2z=6 as the equation and I need help as to what to do next and if that was right, I'm pretty sure next I add that equation with the first? Please help! Thanks!

Answer 1

I like what you did about multiplying the equation by -1 so you can add it (you could have just subtracted) but you need to re-add them. The x's should disappear

Answer 2

What do I re-ad?

Answer 3

You want to add 1 and 3 also 2 and 3 together. The goal is to eliminate a variable so that you are left with 2 equations and 2 variables.

Re-add the equations. You need to start over

Answer 4

okay thank so i should start by adding 1 and 3?

Answer 5

Step 1: Get a variable to have all the same coefficients
( x+y-4z=-7 )*2
2x+3y-3z=-6
2x+2y-z=0

Answer 6

Step 2: Eliminate that variable by subtacting (or adding the opposite if that is easier for you) I am going to subtract 3 from 1 and 2 from 1
1) 2x+2y-8z=-14
2) 2x+3y-3z=-6
3) 2x+2y-z=0

Answer 7

okay so i should multiply the first by 2 alright ill do that all now thanks so much

Answer 8

I's so confused right now how do i get the variable by it's self

Answer 9

1) 2x+2y-8z=-14
3) 2x+2y-z=0
a)-7z=-14

1) 2x+2y-8z=-14
2) 2x+3y-3z=-6
b) -y-5z=-8

Step 3: Now that we have 2 equations and 2 unknowns we can solve for those unknowns. I am going to use substitution
a) -7z=-14
b) -y-5z=-8

a) z=2
b) -y-5(2)=-8
y=-2

Answer 10

Oh! and x would be 3!

Answer 11

after you sub the y into the first equation, right?

Answer 12

Step 4: Using the values we just found we need to plug them into one of the original equations to solve for the last unknown. I always choose the easiest one.
1) x+y-4z=-7
x+(-2)-4(2)=-7
x-2-8=-7
x=3

Answer 13

Thank you so much! I was stuck on that problem forever and you really helped!

Answer 14

Sorry I wasn't reading your comments. Tell me what steps confuse you and I'll try to explain

Answer 15

yw. Do you get it?

Answer 16

yes after you explained the first two on what y and z was I plugged in y and got that x was 3

Answer 17

Yup. Good job. Feel free to tag me in future questions by doing "@ChmE"

Answer 18

I have a small one I'll post in a second.