Solving Equations using the elimination method. Help!

SlowlyFading · 2012-07-04 04:35:34

Hello everybody,

I need the answers to 5 problems and how exactly you got that answer using the elimination method. I want to understand how to do these!

The Questions:
10. y = (2/3)x - 1
y = -x + 4

11. x + y = 0
3x + y = -4

12. 4x + 3y = -15
y = x + 2

13. x + 2y = -4
4y = 3x + 12

14. y = 2x
x + y = 3

Thanks! <3

bobbym · 2012-07-04 04:37:28

Hi;

Look at 11)

x + y = 0
3x + y = -4

What happens when you subtract the bottom equation from the top equation?

SlowlyFading · 2012-07-04 04:44:40

How do you subtract equations like that?

Bob · 2012-07-04 05:14:01

hi SlowlyFading

I'll start with Q11.

11. x + y = 0
3x + y = -4

The amount of 'y' is the same in both equations, so you can eliminate y by subtracting terms.

(x-3x) + (y -y) = 0 - -4

Simplify:

-2x + 0 = 0 + 4 = 4

So -2x = 4 => x = -2

Once you know x, you can substitute that value back into one of the equations to get y.

First equation looks easier so

-2 + y = 0 => y = +2

Finally check this answer by seeing if it fits the other equation:

3x + y = 3 times -2 + 2 = -6 + 2 = -4. That's the amount on the right hand side (RHS) so these values work in both equations.

Bob

SlowlyFading · 2012-07-04 05:22:17

You said, "The amount of 'y' is the same in both equations, so you can eliminate y by subtracting terms.

(x-3x) + (y -y) = 0 - -4"

My question is how do I know whether I'm supposed to subtract or add on that step?

Bob · 2012-07-04 05:28:07

Because I wanted y - y. So I knew subtract would do it. (y + y wouldn't eliminate it)

That question is the easiest to do by elimination.

Most people would use the other method, substitution, for the others, but I'll take you through them by elimination if you want.

Suggest Q14 next.

Bob

SlowlyFading · 2012-07-04 05:33:58

Shouldn't the answer for something like this, be two points?

SlowlyFading · 2012-07-04 05:36:19

All I understand about this type of problem is that;
Step 1. Line up the x's on top of each other, the y's on top of each other, and the the equals signs and the numbers on top of each other.
Step 2. Multiply the equations (if necessary) so that we have a variable with the same coefficient

Besides that I don't understand this.

Bob · 2012-07-04 05:38:51

If the two equations are straight lines, then they will cross at a single point. It would have an x coordinate and a y coordinate and that's what I got.

In coordinate terms it would be (-2,2) but that's only one point not two.

Bob

ps. I'll make a graph and expand this answer. Coming up.

Bob · 2012-07-04 05:40:32

Reply to post 8.

yes, that's the method.

So, do you want the graph or to go through another question (Q14) ?

Bob

SlowlyFading · 2012-07-04 05:46:46

Lets go to 14.

It doesn't ask for graphs but in the lesson's examples it gives the answers as points like this for example (5, -1).

Bob · 2012-07-04 05:50:53

14. y = 2x
x + y = 3

Ok. Step 1 line up the xs, the ys and the numbers.

The second equation is in the right format so leave it as it is.

To get the first equation right you need to subtract 2x from each side of the equation.

Post back what you get.

Bob

SlowlyFading · 2012-07-04 05:57:18

I got 1.

Bob · 2012-07-04 05:58:29

You seem to have jumped forward about 6 steps. But Ok this may be correct. Is that x = 1 or y = 1 ?

Bob

SlowlyFading · 2012-07-04 05:59:51

I believe x = 1

Bob · 2012-07-04 06:02:18

That is correct.

So put that value into y = 2x to find y.

Check it works by x + y = ?

post coord answer (x,y)

Bob

SlowlyFading · 2012-07-04 06:26:19

y = 2

Bob · 2012-07-04 06:37:13

Yes, well done! That's what I got.

I had time to do the graphs anyway.

Bob

I think Q12 is the next easiest.

SlowlyFading · 2012-07-04 06:46:45

Oh, okay. Awesome!

So for 12 I did step 1 so;
2x = y
x + y = 3

Bob · 2012-07-04 06:51:45

Q12

12. 4x + 3y = -15
y = x + 2

Change the format of equation 2.

Then you need to do some multiplying so I suggest you post step 1 only.

Bob

SlowlyFading · 2012-07-04 06:52:45

Wait, wrong numbers

here's step 1 for 12:

12. 4x + 3y = -15
y = x + 2

Becomes

3y + 4x = -15
y = x + 2

Bob · 2012-07-04 06:56:29

You'll have to change y = x + 2.

get the 'x' term on the left then the = then the number.

Bob

SlowlyFading · 2012-07-04 07:03:14

12. 4x + 3y = -15
x + y = 2

Is that correct?

how do i know what equation needs changed or if both need changed?

Bob · 2012-07-04 07:05:37

The format for the elimination method is

The signs may be minus.

y = x + 2 does not become x + y = 2

When you subtract x from each side ...................

Bob

SlowlyFading · 2012-07-04 07:15:53

Wait, are we doing the same thing? I was just trying to line up the x's and y's..

Math Is Fun Forum

#1 2012-07-04 04:35:34

Solving Equations using the elimination method. Help!

#2 2012-07-04 04:37:28

Re: Solving Equations using the elimination method. Help!

#3 2012-07-04 04:44:40

Re: Solving Equations using the elimination method. Help!

#4 2012-07-04 05:14:01

Re: Solving Equations using the elimination method. Help!

#5 2012-07-04 05:22:17

Re: Solving Equations using the elimination method. Help!

#6 2012-07-04 05:28:07

Re: Solving Equations using the elimination method. Help!

#7 2012-07-04 05:33:58

Re: Solving Equations using the elimination method. Help!

#8 2012-07-04 05:36:19

Re: Solving Equations using the elimination method. Help!

#9 2012-07-04 05:38:51

Re: Solving Equations using the elimination method. Help!

#10 2012-07-04 05:40:32

Re: Solving Equations using the elimination method. Help!

#11 2012-07-04 05:46:46

Re: Solving Equations using the elimination method. Help!

#12 2012-07-04 05:50:53

Re: Solving Equations using the elimination method. Help!

#13 2012-07-04 05:57:18

Re: Solving Equations using the elimination method. Help!

#14 2012-07-04 05:58:29

Re: Solving Equations using the elimination method. Help!

#15 2012-07-04 05:59:51

Re: Solving Equations using the elimination method. Help!

#16 2012-07-04 06:02:18

Re: Solving Equations using the elimination method. Help!

#17 2012-07-04 06:26:19

Re: Solving Equations using the elimination method. Help!

#18 2012-07-04 06:37:13

Re: Solving Equations using the elimination method. Help!

#19 2012-07-04 06:46:45

Re: Solving Equations using the elimination method. Help!

#20 2012-07-04 06:51:45

Re: Solving Equations using the elimination method. Help!

#21 2012-07-04 06:52:45

Re: Solving Equations using the elimination method. Help!

#22 2012-07-04 06:56:29

Re: Solving Equations using the elimination method. Help!

#23 2012-07-04 07:03:14

Re: Solving Equations using the elimination method. Help!

#24 2012-07-04 07:05:37

Re: Solving Equations using the elimination method. Help!

#25 2012-07-04 07:15:53

Re: Solving Equations using the elimination method. Help!

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