The objective is to solve system problems of equations by the addition method ( no multiplying required) how would you solve this : 2x+y=3 -2x+5y=-9 have solve for x and y to plot on graph.

- anonymous

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- anonymous

2x + y = 3
-2x + 5y = -9
If you add straight down you get
6y = -6
divide by 6 and you get
y = -1
Then you need to substitute the y = -1 into either one of the original equations.
I will put it into the first one.
2x -1 = 3 add 1 to both sides
2x = 4 divide by two
x = 2
So x = 2 and y = -1

- anonymous

How would you solve for x and y to plot on graph for this equation: 7x-y=12 -3y+7x+8 ?

- anonymous

Do you want to plot this on a graph to solve this?

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## More answers

- anonymous

yes, It's just like the previous question that I asked.

- anonymous

Check your second equation. there is something wrong with it. Then I will help you solve it.

- anonymous

-3=7x+8

- anonymous

Is there no y in that equation?

- anonymous

I'm sorry, it's -3y=7x+8

- anonymous

7x - y = 12 and -3y = 7x + 8 (First thing is to get the x's and y's on the same side.

- anonymous

7x - y = 12
-7x - 3y = 8 (I subtracted 7x from both sides)

- anonymous

7x - y = 12
-7x - 3y = 8 (Notice if you add straight down your x's are gone)
-4y = 20 (Added the two equations together)
y = -5 (Divide both sides by -4)
Put y = -5 into 7x - y = 12
7x - (-5) = 12
7x + 5 = 12
7x = 7
x = 1
So... x = 1 and y = -5

- anonymous

same thing here: y=3x+13 2x=y-9 solve for x and y and plot on graph.

- anonymous

Put the x's and y's on the same side with the number on the other side... What do you get?

- anonymous

Is it 5x and 2y=4?

- anonymous

If you take y = 3x + 13 How do you get the 3x on the side with the y?

- anonymous

do you sub. 3x to move it?

- anonymous

Yes... so you get -3x + y = 13
Now the second equation 2x = y - 9 how do you get the y over with the 2x?

- anonymous

subtract y to move it

- anonymous

Yes.. so now you have 2x - y = -9
Now write both of those equations over each other.

- anonymous

-3x + y = 13
2x - y = -9
And you get this ... ok?

- anonymous

ok, then what do I do I know that I sub. and get -x=4 is this correct?

- anonymous

Well... you actually add but yes you get
-x = 4 so to solve for x when x is negative you simply take the opposite of both sides.
So the opposite of "negative x is positive x" and the opposite of "positive 4 is negative 4"
x = -4

- anonymous

Now we are going to substitute x = - 4 into one of the equations.
Let's use the y = 3x + 13
so.. y = 3(-4) + 13
y = -12 + 13
y = 1
So x = -4 and y = 1

- anonymous

last problem: 4x + 12 = -7y -y +12= 4x solve for x and y to plot on graph.

- anonymous

Get x's and y's on the same side with the number on the other. What would you get for
4x + 12 = -7y

- anonymous

4x-7y+12

- anonymous

Well you need an = sign in this problem... Bring the -7y over to the 4x and take the 12 to to the other side. What do you get?

- anonymous

I meant 4x-7y=12

- anonymous

If it is -7y on the right side you add 7y and it becomes + 7y on the left side.
If it is + 12 on the left side you - 12 from both sides and it becomes -12 on the right side.

- anonymous

So you get 4x + 7y = -12
Try the 2nd equation
-y + 12 = 4x

- anonymous

-4x+y=-12

- anonymous

Close.. You -4x which is correct, you - 12 which is correct.. but if you look at the 2nd equation is says "-y" on the left side so it needs to stay "-y" on the left side.
-4x - y = -12
Now put those two over each other.. add... and tell me what you get.

- anonymous

y=-4

- anonymous

You should have gotten
-6y = -24
Then you divide by -6 and you get
y = 4
Now put y = 4 into one of the equations... Let's pick 4x + 12 = -7y

- anonymous

x=4

- anonymous

You should have gotten
4x + 12 = -7(4)
4x + 12 = -28
subtract 12 from both sides
4x = -40
divide by 4
x = -10
So the answers are x = -10 and y = 4

- anonymous

that can't be right because the puzzle I'm doing leaves me with the letter d which is x=4 and y=-4 to spell out a sudden debt payoff.

- anonymous

OK Let me do it again.

- anonymous

4x + 12 = -7y -y +12= 4x
4x + 7y = -12 -4x - y = -12
4x + 7y = -12
-4x - y = -12
6y = -24
y = -4
4x + 12 = -7(-4)
4x + 12 = 28
4x = 16
x = 4
You are correct x = 4, y = -4
Look thru my answer here... This is important you know how to do these because they are going to get harder on the next lesson and if you don't get this well, you won't get the next step.
Study hard.... it pays off :-)

- anonymous

Thanks a lot I've got another sheet to do later maybe I'll get you again to help me. Is there a way I can ask for you personally?

- anonymous

Sure.. you can email me at amcbeth328@gmail.com

- anonymous

You were a great help. I'm not that great at math. I have a 62 average and my teacher told me that I have to get at least a 78 this 4 weeks or I will have to go to recovery school this summer.

- anonymous

I can tell you are weak... I would be glad to help you as long as you want to learn and not just want answers, because in the long run, you will get deeper and deeper into not getting it and it will hurt you in the long run.

- anonymous

I'm not looking for answers. I just don't understand how to do the problems sometimes and my teacher is so busy she doesn't have time to be one on one with to explain how to do them. I have always been weak in math but this year is really kicking me in the butt. I would go to tutoring but we don't have a car and no one in school will give me a ride home so therefore I'm kind of stuck trying to figure this stuff out on my own. It's been a long time since my parents were in school so they can't help me much.

- anonymous

Write me anytime.

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