# Thread: Solve system by elimination

1. ## Solve system by elimination

How do you Solve a system by elimination? Please explain how you get the answer. Thanks in advance!

Problem:
Solve each system by elimination

-a + b -c = -5
6a + 5b + 2c = 9
-3a -2b -c = -3

2. Originally Posted by MajorGriffin
How do you Solve a system by elimination? Please explain how you get the answer. Thanks in advance!

Problem:
Solve each system by elimination

-a + b -c = -5
6a + 5b + 2c = 9
-3a -2b -c = -3
multiply the first line by 6 and add it to the second (write down what you've got) multiply it again by -3 and add it to the third (write what you've got).
now leave the first line intact,you just used it to eliminate and write down the two lines that you've got.

3. Originally Posted by Raoh
multiply the first line by 6 and add it to the second (write down what you've got) multiply it again by -3 and add it to the third (write what you've got).
now leave the first line intact,you just used it to eliminate and write down the two lines that you've got.
Okay, so.
Multiplied the top line by 6
Got -6a+6b-6c=-30 correct?
added it to the second line and got
11b-4c=-21 (the a's canceled out)
multiplied that by -3 and got:
-33b + 12c = 63 (Is this right so far?) Because then you say to leave the first line intact (-a + b - c = -5) and write down the two lines left would it look something like...

-a + b - c = -5
11b - 4c = -21
-33b + 12c = 63

I'm not sure what this is supposed to look like as a final answer. I just followed your instructions the best I could

4. Originally Posted by MajorGriffin
Okay, so.
Multiplied the top line by 6
Got -6a+6b-6c=-30 correct?
added it to the second line and got
11b-4c=-21 (the a's canceled out)
multiplied that by -3 and got:
-33b + 12c = 63 (Is this right so far?) Because then you say to leave the first line intact (-a + b - c = -5) and write down the two lines left would it look something like...

-a + b - c = -5
11b - 4c = -21
-33b + 12c = 63

I'm not sure what this is supposed to look like as a final answer. I just followed your instructions the best I could
Almost but not quite.
you should use the first line to ELIMINATE.and DON'T Touch it.
so you multiply it by 6 to eliminate $\displaystyle a$ of the second line.
and You didn't multiply it by -3 to eliminate $\displaystyle a$ of the third line.

5. I don't understand what you mean

6. Originally Posted by MajorGriffin
I don't understand what you mean
it's Gauss elimination method.

7. $\displaystyle \left\{\begin{matrix} -a+b-c=-5\\ 6a+5b+2c=9\\ -3a-2b-c=-3 \end{matrix}\right.$$\displaystyle \Leftrightarrow \left\{\begin{matrix} -a+b-c=-5\\ 11b-4c=-21\\ -5b+2c=12 \end{matrix}\right.$$\displaystyle \Leftrightarrow \left\{\begin{matrix} -a+b-c=-5\\ 11b-4c=-2\\ c=\frac{12+5b}{2} \end{matrix}\right.$
now use substitution to find b.
hope that helps.

8. Okay thanks for clearing that up!