Solve the systems using substitution.
6x + 2y = 0
4x + y = -1
3x + 2y = -4
x + 2y = -8
5x - 4y = 14
x - 2y = -2
x + 3y = -4
4x + 5y = 5
x + 3y = -5
2x - y = 18

- anonymous

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- mathmale

One problem per post, please. Which one will it be for this post?

- anonymous

6x + 2y = 0
4x + y = -1

- mathmale

You are to use the subst. method. Choose one of these 2 equations and solve it for y. Which equation would you choose for this, and why?

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## More answers

- anonymous

6x + 2y = 0 This one seems a bit more simpler

- mathmale

OK. But I'd choose the 2nd one, because solving for y is easier than solving an equation in 2y for y.
so: Let's solve 6x+2y=0 for y.
Start by dividing all 3 terms by what number?

- anonymous

6? That or zero.

- mathmale

Can't divide by zero, so zero is out.
I'd suggested that we solve the 1st equation for y. That means focusing on the y term, not the x term.
Divide all 3 coefficients of your equation by 2. What do you obtain?

- anonymous

3x+y=0

- mathmale

Good. Now, please solve that resulting equation for y.

- mathmale

All you have to do is to subtract 3x from both sides of the equation.

- anonymous

So subtract 3x from 3x and 0?

- mathmale

Yes. 3x-3x=0;. 0-3x = -3x

- mathmale

What's left?

- anonymous

y=-3?

- mathmale

You have to include that ' x ' also.
3x + y = 0
-3x -3x
---------------
y= ?

- anonymous

-3x

- mathmale

Better.
y=-3x.
what is the second equation? Type it out now, as is.

- anonymous

4x + y = -1

- anonymous

Oh wait, sorry, let me fix it

- anonymous

4x + -3x = -1

- mathmale

it's best not to write " +- " Combine these 2 signs: (-1)(1)=?

- mathmale

Then re-write your equation.

- anonymous

Im a bit confused by what your asking, really sorry

- mathmale

You have written 4x + -3y = -1. The " + - " is not acceptable; simplify it to just - .

- anonymous

Oh ok. 4x -3x = -1
like that?

- mathmale

Much better.
Now combine the 2 x terms on the left side of your equation.

- anonymous

-1x=-1

- mathmale

But isn't 4x - 3x = +x ?

- anonymous

so.... -1x=x?
Im sorry this is taking so long, I got really nobody around to explain any of this to me

- mathmale

that's what I'm here for. ;)
4x - 3x = +x.
Therefore your equation 4x - 3x = -1 becomes x = -1.
OK with this?

- anonymous

Im pretty sure.

- mathmale

We've already found that y=-3x.
To find the numerical value of y, please substitute (-1) for x in this equation and compute the value of y. y=?

- anonymous

-4 - 3 = +x.

- anonymous

Srry if thats wrong

- mathmale

formula for y: y=-3x. Known value for x: x=-1
substituting x=-1 into y=-3(x), y=-3(-1) = ? (Note: Multiply, not + or - )

- anonymous

Im getting confused :(

- mathmale

I'm sorry. We're going to go thru this problem again.
First, let's do it a different way, that might be faster.

- anonymous

Ok

- mathmale

6x + 2y = 0 is the first equation; 4x + y = -1 is the second.

- mathmale

If we use the second equation instead of the first, we won't have to divde the y term by 2.
The first equation has a y-term of 2y; the second equation has a y-term of just y.
So, it makes sense to solve the 2nd equation for y, not the first.

- anonymous

Ok

- mathmale

If the 2nd equation is 4x + y = -1, all we have to do is to subtract 4x from both sides.
Can you do that?
4x + y = -1
-4x = -4x
-------------------
Please combine these equations to obtain a simpler, new one.

- anonymous

x+y=3x?
or do we just remove that first x?

- anonymous

Oh wait no.

- anonymous

x+y=-5x

- mathmale

Note: 4x
-4x
------
0. Therefore, we get
4x + y = -1
-4x -4x
-----------------
0 = y = -1-4x
or y= -1 -4x.

- mathmale

are you OK with this, or does it need further discussion?

- anonymous

So right now we got 0 - y = -5x?

- mathmale

that's 0 + y = -1 - 4x, or simply y = -1 - 4x.

- mathmale

The -1 and the -4x are NOT like terms, so can't be combined.
-1 - 4 = -5 YES
but
-1 -4x is not -5x; it stays as -1 - 4x.

- anonymous

Oh ok. And we already know what x is from the other problem

- mathmale

Don't remember!
We have to substitute this y = -1 -4x into the other equation, so we end up with
6x + 2 (-1-4x) = 0 which is an equation in x alone (no y).
6x - 1 - 4x = 0. OK? If not, ask questions.

- anonymous

Can you explain that in a bit easier way?

- mathmale

Sorry...I've made a number of typing mistakes which probably have made this even more difficult for you. I'd suggest we just stick with our previous solution and move on to another problem.

- anonymous

Oh ok. So for this problem can you paste into a reply what I put down? all these different ones are confusing me :(

- mathmale

We got 4x - 3x = -1, which translates into x = -1. Then, knowing that y=-3x, we got y =3. so, the solution is (-1,3).
I'd love to copy and paste, but my computer is not allowing me to do so at the moment.
I will go thru this problem with yo u again later if y ou like.
but for now, would you please pick anotehr problem to work on? How many such problems do you have left to do?

- anonymous

3x + 2y = -4
x + 2y = -8
After this one I got 3 more

- mathmale

Look at the 2nd equation. Since the coefficient of x is 1, I think we should solve this equation for x, not the other equation.
if x + 2y = -8, let's subtract 2y from both sides to isolate the y term:
-2y -2y
--------------
x = ??

- anonymous

-6y?

- mathmale

We have -8 - 2y on the right side.
-8 and -2y are NOT "like" terms in that one has y, the other does not.
Thus, we cannot combine the -8 and the 2 to get 6.
Again, the final result is x= -8 - 2y.
Can you accept this? If not, ask questions.

- mathmale

@Pingurox ?

- anonymous

Sorry, had to feed my dog

- anonymous

And yes, I can accept that

- mathmale

Since you can review this conversation later, please accept that x= -8 -2y.
Next, we substitute this into the other equation: 3x + 2y = -4.

- mathmale

3( ) + 2y = -4
Please write -8-2y inside this set of parentheses.

- anonymous

3(-8-2y ) + 2y = -4

- mathmale

Yes. Good. Multiply each term -8 -2y by 3. What do you get? (Leave the other terms alone)

- anonymous

So multiply -8 -2y by 3 each?

- mathmale

Yes. that's the "Distribution Rule of Multiplication."

- anonymous

So I multiple them seperately or together?

- mathmale

Multiply the -8 by 3.
Separately, multiply the -2y term by 3.

- mathmale

Separately. And keep the products (answers) separate.

- anonymous

-8 by 3.= -24
-2y by 3. =-6y

- mathmale

Right. So, on the left side of your equation,
you have
-24 - 6y +2y = -4.
Combine the -6y and the -2y on the left, to form just one term with y in it.

- mathmale

-6y+2y = ? (note that you have 2 different signs here).

- anonymous

Uhh....im a wee bit lossed

- mathmale

-6+2=-4, so
-6y+2y = -4 y.
Then, on the left side y ou have -24 - 4y=-4.
Adding 24 to both sides eliminates the -24 on the left and results in
-4y=-4+24, or -4y=20
Can y ou now find y?

- mathmale

If -4y=20, divide both sides by -4.

- anonymous

divide -4y and 20 by -4?

- mathmale

Yes. -4y divided by -4 is simply y. We want y alone on the left side.
So, now on the left side we have y, and on the right side we have 20 / (-4), or

- mathmale

\[\frac{ 20 }{ -4 }=?\]

- mathmale

What is 20 divided by -4?

- mathmale

20 divided by 4 is 5.
The only thing different in our "what is 20 divided by -4" is that the 4 is negative.
20/4=5, 20 / (-4) = ??

- anonymous

-5

- mathmale

right.
So, on the left of our equation we now have y and on the right side we have -5.
Therefore, y = -5.
You can substitute y=-5 into either of the 2 given equations to find x.
suppose we choose to use the equation x+2y=-8. Substituting y = -5,
x + 2(-5) = - 8
What is 2(-5), if we multiply?

- anonymous

-10

- mathmale

Yes, and so you have x - 10 = -8
and you need to add 10 to both sides to obtain a value for x.
Finish this, please:
x - 10 = -8
+10 = +10
________________
x = ?

- anonymous

x-20=-18
Im just gueesng....x=-2?

- mathmale

On the right side you have -8 + 10, and that comes out to just 2.
Therefore, x = 2. Earlier, we found that y =-5
Therefore your solution is (2,-5). x=2 and y=-5.
These 2 equations have graphs which are straight lines.
If you were to graph them you'd see that they intersect at the point (2,-5).

- anonymous

Alright. So just copy paste that into my worksheet for my solution?

- mathmale

You can do that, of course. But I'd feel better if you'd not just accept this result as our answer, but rather check it by substitution.
You can substitute x=2 and y=-5 into either equation. If the equation is then true, your solution is correct; otherwise it is not correct.

- mathmale

I encourage you to try this!
I've done it myself and find that the first equation is true when x=2 and y=-5.
But it's important that y ou know how to do this for ourself.

- mathmale

@Pingurox: I'm sorry but my head is swimming after hours on OpenStudy. I need to get off OpenStudy.
I hope you'll go through our solution of the 2nd problem again and make a list of any questions you may have about that process. We could discuss your questions later. But I have to excuse myself right now. Best of luck to you, and thanks for your persistence.

- anonymous

No problem. I gtg anyways

- anonymous

anybody still there

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