Question

Determine the solution for the system of equations below:
2x+3y =5
4y-3x=18

Answer 1

oops my bad...thought that was 4x - 3y on the 2nd equation..not 4y-3x. That complicates things a bit. We can still use elimination. We need to multiply each equation by something before adding them together. Can you think of some good numbers to multiply each equation by so that when we add them together one of the variables will vanish?

Answer 2

2 for the top one and 3 for the bottom one?

Answer 3

2x + 3y = 5
-3x + 4y = 18

Subtract the second equation from the first:

-5x + y = 13
y = 13 + 5x

Using substitution:

2x + 3(13 + 5x) = 5
2x + 39 + 15x = 5
17x + 39 = 5
17x = 5 - 35
17x = -34
x = -34/17
x = -2

Substitute x back in to original equation to find y

Answer 4

You don't always have to multiply top and bottom to solve these. It only makes the equations unnecessarily bigger than they need to be.

Answer 5

hero..i thought the idea on this website was to walk people through the steps slowly and interactively...not just post the soloution like that. Several people here have told me so over the past couple of days.

Answer 6

That was a walk through. Nobody said it had to be "slow". And it's not the full solution. I was demonstrating a process different from the norm. That's why.

Answer 7

Furthermore, I'm not here to explain myself to you. I'm here to help the user.

Answer 8

check messages

Answer 9

Why is y = 13 + 5x? Where did the 13 come from?

Answer 10

(4y - 3y) - (3x + 2x) = 18 - 5
y - 5x = 13
y = 13 + 5x

Answer 11

Subtract the first equation from the second...

Answer 12

2x + 3y = 5
-3x + 4y = 18
Multiply the first one by 3 and the 2nd one by 2 to get
6x + 9y = 15
-6x + 8y = 36 Those are not BIG equations!
_________________ Add em together
0x + 17y = 51
17y = 51
y = 3
Now plug in y=3 into either equation to get x.\
MUCH easier than Hero's approach in my opinion

Answer 13

It only APPEARS easier.

Answer 14

You skipped a lot of steps

Answer 15

You multiplied to get your result. I subtracted.

Answer 16

y=3, x=-2

Answer 17

My method is much more useful when the numbers get unreasonably bigger.

Answer 18

Yes @staldk3, my method produced x...
@BangkokGarrett method produced y...

Answer 19

So I guess you were able to find your x and y

Answer 20

Yes.

Answer 21

Thanks

Answer 22

@BangkokGarrett , I didn't say they were HUGE equations, I just said that multiplying made them unnecessarily bigger than they needed to be. In other words, what I was suggesting is that it is not necessary to multiply both equations to find the result.