Question

Solving Systems by Elimination. I don't know how to solve for y. I'll post my problem.

Answer 1

2x + 5y = 17
6x - 5y = -9

Answer 2

I know x = 1 but, how do I solve for y after plugging into x? Dividing is what I have a hard time, like when one of the numbers become a fraction...that's really confusing. :/

Answer 3

You must do better than that.

Start here: 2x + 5y = 17

Solve that for y.

Answer 4

Ohh. So, y = 3. I was told to do it to the 2nd equation.

Answer 5

Is there a way to do it to the 2nd equation?

Answer 6

It matters not. Let's forget about x = 1 for a moment. Where did you get that, anyway?

If you are going to use "Substitution"m you must pick an equatin and solve it for one f the variables. For this cause, I said, solve this for y...

2x + 5y = 17

Do that, first.

Answer 7

No, not substitution. Elimination.

Answer 8

Look at that! Did you just change it or am I going blind?

2x + 5y = 17
6x - 5y = -9

It is most convenient, because we have to do nothing, to "eliminate" the y. We can just add the two equations. What do you get for that?

Answer 9

Haha. It's okay, we all make mistakes. So, adding the equations would be 8x = 12?... o.o That makes no sense to me..

Answer 10

Wait....no...8x = 8...... I was thinking 19 and -7. Haha!

Answer 11

That's probably because \(17 - 9 = 8 \ne 12\)

Ar you happier with \(8x = 8\). That's easy to solve for x, right?

Answer 12

x = 1.

Answer 13

Ding!!! That is a prize-winner. Now we have two good possibilities. Since we are trying to find a simultaneous solution, it shoudl not matter which equation we use to find y. Let's do them both, now that we know x = 1.

2x + 5y = 17
6x - 5y = -9

Substituting the known value, x = 1, we have

2(1) + 5y = 17
6(1) - 5y = -9

Solve both for y and see what you get.

Answer 14

So, "y" should equal 3. Correct? :o

Answer 15

Well. For the 2nd equation...no.. :/

Answer 16

Are you guessing or did you prove it?

Answer 17

6(1) - 5y = -9

6 - 5y = -9

-5y = -15

y = 3

Answer 18

I proved it on scratch paper:

2(1) + 5y = 17.
2 + 5y = 17.
-2 -2
------------
5y = 15.

So y = 3.

Answer 19

Ah, now I realize the 2nd equation makes more sense to me now..*Gives a Medal* :)

Answer 20

Please notice how this order of solution was arbitrary. We did x first because it looked most convenient. There is absolutely nothing wrong with finding y first.

Out two equations:

2x + 5y = 17
6x - 5y = -9

Multiply the top equation by -3

-6x - 15y = -51
6x - 5y = -9

Now add the two equations.

-20y = -60

And out pops y = 3.

Keep your eyes open and don't get stuck in one way of thinking. Good work.

Answer 21

Ahhh. Okay. Well, thank you so much! I was stressed for days on something I have not learned yet from Algebra 1. This is such a relief.