Question

(Three Variable Systems with Elimination)

Solve each system by elimination. Check your answers.

6q - r + 2s = 8
2q + 3r - s = -9
4q + 2r + 5s = 1

I just learned how to do this today in class. I pretty much understand how to do it, but I think I made a silly mistake somewhere. I started getting s = -21/17 and I was like "I don't think this is right..."

Thanks SOOOO much in advance!! :)

Answer 1

q= 1/2
r = -3
s =1

Answer 2

@surdawi You need to explain it. That doesn't help

Answer 3

@ChmE do you want to explain it or you want me to

Answer 4

You go ahead

Answer 5

6q - r + 2s = 8 ===> r = 6q +2s -8
2q + 3r - s = -9 ====> s =2q +3r +9 ===> s =2q +3(6q +2s -8) +9 ===> s=-4q+3
4q + 2r + 5s = 1

4q + 2(6q +2(-4q+3) -8) + 5(-4q+3) = 1
11 - 20q = 1
q=1/2

now plug in
s=-4q+3
s=-4*1/2+3=1

r = 6q +2s -8
r=6*1/2+2*1-8
r=-3

Answer 6

That is the substitution method. The question is asking for elimination.

Answer 7

damn i did it using matrices at the beginning

Answer 8

Yeah I can only use elimination haha! :)

Answer 9

@ChmE your turn bro

Answer 10

1) 6q - r + 2s = 8
2) 2q + 3r - s = -9
3) 4q + 2r + 5s = 1

STEP 1

Lets use 1) and 2) first
1) 6q - r + 2s = 8
2) (2q + 3r - s = -9)2

6q - r + 2s = 8
4q + 6r - 2s = -18
Add them
10q + 5r = -10

Answer 11

STEP 2

Eliminate the same variable
1) (6q - r + 2s = 8)5
3) (4q + 2r + 5s = 1)-2

1) 30q - 5r +10s = 40
3) -8q + -4r + -10s = -2
Add them
22q - 9r = 38

Answer 12

STEP 3

Put our new equations with only 2 variables together in one system
A) (10q + 5r = -10)9
B) (22q - 9r = 38)5

A) 90q + 45r = -90
B)110q - 45r = 190
add them
200q = 100
q = 1/2

Answer 13

STEP 4

Now that we know q we can plug it in to equation A) or B) to solve for r.

STEP 5

Now that we have q and r, we can plug them into 1), 2), or 3) to get s

Answer 14

Did that make sense?

Answer 15

For Three Variable Systems with Elimination eliminate a variable in 1 & 2 and the same in 2 & 3. It should work for 3 & 1 and 3 & 2 as well. You just have to do double elimination, then eliminate one last time with your 2 new equations. It's a pain

Answer 16

@ChmE thank you SOOOOOOO much!!!! Really helped a ton :)

Answer 17

It really is a pain, it takes FOREVER!

Answer 18

@ChmE Wait I can't do what you said, I have to make the first two equations cancel out a variable.
For example,
1) (6q - r + 2s = 8)
3) (4q + 2r + 5s = 1)

I would have to multiply 2 by like 2 to make it
12q - 2r + 4s = 16
so it would 2r would cancel out when I added +2r to it from the other equation.