Question

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

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

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?

Answer 6

6? That or zero.

Answer 7

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?

Answer 8

3x+y=0

Answer 9

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

Answer 10

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

Answer 11

So subtract 3x from 3x and 0?

Answer 12

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

Answer 13

What's left?

Answer 14

y=-3?

Answer 15

You have to include that ' x ' also.

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

y= ?

Answer 16

-3x

Answer 17

Better.
y=-3x.

what is the second equation? Type it out now, as is.

Answer 18

4x + y = -1

Answer 19

Oh wait, sorry, let me fix it

Answer 20

4x + -3x = -1

Answer 21

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

Answer 22

Then re-write your equation.

Answer 23

Im a bit confused by what your asking, really sorry

Answer 24

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

Answer 25

Oh ok. 4x -3x = -1

like that?

Answer 26

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

Answer 27

-1x=-1

Answer 28

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

Answer 29

so.... -1x=x?

Im sorry this is taking so long, I got really nobody around to explain any of this to me

Answer 30

that's what I'm here for. ;)

4x - 3x = +x.

Therefore your equation 4x - 3x = -1 becomes x = -1.
OK with this?

Answer 31

Im pretty sure.

Answer 32

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=?

Answer 33

-4 - 3 = +x.

Answer 34

Srry if thats wrong

Answer 35

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 - )

Answer 36

Im getting confused :(

Answer 37

I'm sorry. We're going to go thru this problem again.

First, let's do it a different way, that might be faster.

Answer 38

Ok

Answer 39

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

Answer 40

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.

Answer 41

Ok

Answer 42

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.

Answer 43

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

Answer 44

Oh wait no.

Answer 45

x+y=-5x

Answer 46

Note: 4x
-4x
------
0. Therefore, we get


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

or y= -1 -4x.

Answer 47

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

Answer 48

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

Answer 49

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

Answer 50

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.

Answer 51

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

Answer 52

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.

Answer 53

Can you explain that in a bit easier way?

Answer 54

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.

Answer 55

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

Answer 56

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?

Answer 57

3x + 2y = -4
x + 2y = -8

After this one I got 3 more

Answer 58

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 = ??

Answer 59

-6y?

Answer 60

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.

Answer 61

@Pingurox ?

Answer 62

Sorry, had to feed my dog

Answer 63

And yes, I can accept that

Answer 64

Since you can review this conversation later, please accept that x= -8 -2y.

Next, we substitute this into the other equation: 3x + 2y = -4.

Answer 65

3( ) + 2y = -4

Please write -8-2y inside this set of parentheses.

Answer 66

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

Answer 67

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

Answer 68

So multiply -8 -2y by 3 each?

Answer 69

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

Answer 70

So I multiple them seperately or together?

Answer 71

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

Answer 72

Separately. And keep the products (answers) separate.

Answer 73

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

Answer 74

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.

Answer 75

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

Answer 76

Uhh....im a wee bit lossed

Answer 77

-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?

Answer 78

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

Answer 79

divide -4y and 20 by -4?

Answer 80

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

Answer 81

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

Answer 82

What is 20 divided by -4?

Answer 83

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) = ??

Answer 84

-5

Answer 85

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?

Answer 86

-10

Answer 87

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 = ?

Answer 88

x-20=-18

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

Answer 89

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).

Answer 90

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

Answer 91

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.

Answer 92

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.

Answer 93

@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.

Answer 94

No problem. I gtg anyways

Answer 95

anybody still there