Question

Solve the following system of equations:

x - 2y = 14
x + 3y = 9

(1, 12)
(-1, -12)
(12, -1)
(12, 1)

Answer 1

What have you tried? Give us something to go on?

Answer 2

ive tried nothing

Answer 3

Well, that's no good. You MUST have learned or heard of SOME sort of technique to solve this. Throw me a bone...

Answer 4

do i have to multiply?

Answer 5

to start

Answer 6

Maybe. I'm tempted to multiply the second equation by -1. Try it.

Answer 7

how uhh how would i set that up?

Answer 8

It's already set up. You just have to do it.

x - 2y = 14
x + 3y = 9

Multiply second equation by -1

x - 2y = 14
-x - 3y = -9

That's it. You could have done that.

Answer 9

36?

Answer 10

36 what? What did you do next? This is what "show your work" is all about.

x - 2y = 14
-x - 3y = -9

One thing at a time. What's next? SHOW IT! Don't try to leap all the way to the end.

Answer 11

i did -x - 3y = -9
and got 36

Answer 12

That makes no sense. You do not know the values for x and y. Where did the other equation go?

x - 2y = 14
-x - 3y = -9

I multiplied the second equation by -1 for a reason. ADD the two equations.

x - x = 0

-27 - 3y = What?

14 - 9 = What?

Answer 13

im so confused i dont get this at all

Answer 14

Do you understand x - x = 0?

Answer 15

yeah

Answer 16

Typo on the next one. Sorry about that.

How about -2y - 3y = -5y -- Make sense?

Answer 17

what do you do for the y

Answer 18

Here's where we were.

x - 2y = 14
-x - 3y = -9

Think about the vertical arrangement. The x in one is over the x in the other.
The y in one is over the y in the other. The constant term on the other side of "=" is lined up. Do you see these relationships?

Answer 19

alright now lets do the question

Answer 20

We're trying. Do you see the relationships I have described?

Answer 21

yes i think so

Answer 22

Perfect. Now, consider the two stacked equations as three separate addition problems.

Add the x terms.
Add the y terms.
Add the constant terms.

You should get three results - one for each vertical problem.

Answer 23

which 3 do i do

Answer 24

The three vertical problems, as I described them in the last post.

Answer 25

Have you heard of the "Substitution Method"?

Answer 26

no

Answer 27

but tbh i kind of need the answer the test might time out

Answer 28

If you have not EVER heard of ANY method to solve this problem, you should get it wrong so that you can receive proper placement for your next class. It is not fair for you to have been given such a problem with NO expectation of solving it - unless this is a placement test. If this is a placement test - or any other kind of test - you should not be asking for help in this forum.