Question

Use a matrix to find a solution to the system of equations:
-8x-8y=-16
6x-9y=-108

Answers:
(-6,8)
(6,8)
(8,-6)
(6,-8)

Answer 1

Please explain! I'm really stuck, my teacher didn't explain matrices well and I have no idea how to solve this....

Answer 2

@Hero please help!

Answer 3

I saw this exact same question before and I answered it as well.

Answer 4

Oh...

Answer 5

well can you please help me? <3

Answer 6

Okay, I know how to solve it using Gaussian Elimination method

Answer 7

Which do you use..

Gaussian Elimination
Ax = B
or
Cramer's Rule?

Answer 8

Um I have no idea what either of those are....my teacher is kind of bad

Answer 9

I know what eliminations is, but I've never heard of Gaussian Elimination

Answer 10

Okay, what about Reduced Row Echelon Form?

Answer 11

yeah, that's where it ends up being all 1s and 0s with the constant on the right side, correct?

Answer 12

Yes, good. That's the one that I am comfortable with because it is easy.

Answer 13

okay, that works for me

Answer 14

So basically, you have this
\[\left[ \begin{matrix} -8 & -8 & -16 \\ 6 & 9 & 108 \end{matrix} \right] \]

Answer 15

yes

Answer 16

The first thing you can do is divide the first row by -8 and the second row by 3. When you do that you will get:
\[\left[ \begin{matrix} 1 & 1 & 2 \\ 2 & 3 & 36 \end{matrix} \right]\]

Answer 17

Now from there, you can multiply the 1st row by 2, then subtract Row 2 - 2*Row 1:
\[\left[ \begin{matrix} 1 & 1 & 2 \\ 0 & 1 & 32 \end{matrix} \right]\]

As you can see...we're getting closer :)

Answer 18

so all we need is to get the last 0?

Answer 19

now simply take row 2 and subtract it from row 1 to get:
\[\left[ \begin{matrix} 1 & 0 & -30 \\ 0 & 1 & 32 \end{matrix} \right]\]

Answer 20

alright!
now we have
x=-30
y=32

Answer 21

Yes, correct

Answer 22

so how do we get to 6 and 8?
the MC answers are
(-6,8)
(6,8)
(8,-6)
(6,-8)

Answer 23

yeah, that's what I got the first time I solved this

Answer 24

Hang on...

Answer 25

the bottom row simplifies to
2 -3 -36

Answer 26

start with
6x-9y=-108

6 - 9 -108
divide by 3
2 -3 -36

so your matrix is

1 1 2
2 -3 -36

now try again

Answer 27

That's where I made the mistake...

Answer 28

My original matrix is wrong I thought it was + 9

Answer 29

okay, so we start over from there?

Answer 30

Not to worry @HelennnnnnC I won't leave you hanging

Answer 31

Thank you <3 :)

Answer 32

I hope that link helps you out. I made sign errors while attempting to solve this time. But the correct solution is in that link above.

Answer 33

http://openstudy.com/updates/523c759be4b00182897ef708

Answer 34

\[\left[ \begin{matrix} -8 & -8 & -16 \\ 6 & -9 & -108 \end{matrix} \right]\]
Divide the first row by 8, the second row by 3:
\[\left[ \begin{matrix} 1 & 1 & 2 \\ 2 & -3 & -36 \end{matrix} \right]\]
Then you could subtract R3 -2R1:
\[\left[ \begin{matrix} 1 & 1 & 2 \\ 0 & -5 & -40 \end{matrix} \right]\]
Then divide row 2 by -5 to get:
\[\left[ \begin{matrix} 1 & 1 & 2 \\ 0 & 1 & 8 \end{matrix} \right]\]
Afterwards you could subtract R1 - R2:
\[\left[ \begin{matrix} 1 & 0 & -6 \\ 0 & 1 & 8 \end{matrix} \right]\]

Answer 35

Okay, sorry...unfortunately this site doesn't make it any easier for you to correct a mistake when you type using \(LaTeX\) so it took me that long to fix it.

Answer 36

thank you sooo much! <3