Question

I have tried this several times but can't solve it. Can you guys explain it to me?

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = −2

x = 0

x = 2

There is no x value as there is no solution.

x can be any value as there is an infinite number of solutions.

Answer 1

Uh, did you just post the entire answer sheet to the quiz?

Answer 2

'cause I don't want this, I just need someone to explain HOW to do the problem.

Answer 3

@Hero can you help?

Answer 4

Anyone there?

Answer 5

Divide both sides of the second equation by 2

Answer 6

OK, hang on.

Answer 7

Sorry I'm a little slow, but in Substitution method don't you subtract the 2x in the first equation so you get Y = 1 - 2x? which you then substitute into the second equation??

Answer 8

@studygirl, I was getting to that. However, there is a reason I wanted to you divide both sides of the second equation by two first.

Answer 9

OK give me a minute and I'll do it. :)

Answer 10

you divide 4x, 2y, and -2 all by 2? Sorry math isn't my strong suit

Answer 11

Yes, let me know what you get afterwards.

Answer 12

ok 1 second. :)

Answer 13

2x + 1y = -1 ??

Answer 14

Okay which means you are left with the following system:

2x + y = 1
2x + y = -1

Answer 15

OK what do I do now?

Answer 16

Now from that what observations can you make about the system?

Answer 17

well they seem identical except that the first on is 1 and the second is -1.

Answer 18

Yes the left sides are the same but the right side isn't. That basically tells you that this system is inconsistent (has no solution)

Answer 19

So in essence, there is really no point in trying to solve this system. Even if you tried substitution, it wouldn't work. But if you wish to satisfy your own curiosity, you can try solving by substitution just to see what happens.

Answer 20

Sorry my computer is acting up a bit. :)

Answer 21

so is there no solution? or infinite solutions?

Answer 22

You can only have infinite solutions if both equations are the same or are multiples of each other.

Answer 23

so no solutions?

Answer 24

If you had something like

2x + y = 1
4x + 2y = 2

This system would have infinite solutions because 4x + 2y = 2 is a multiple of
2x + y = 1

Try to understand why this is the case.

Answer 25

OK, so I'll admit I'm a little lost as to the answer. Sorry. :(

Answer 26

It probably would be good if you went ahead in your original direction by using substitution as instructed by the problem. You were correct using the first equation you came up with y=1-2x.

Substituting this in the 2nd equation you would get: 4x +2(1-2x) = -2 then continuing
4x + 2 -4x = -2
2=-2 An inconsistency which means there is no solution. this is of course what Hero came up with by looking at the system as whole.

Answer 27

There is no solution to your system (as I had already stated above)

Answer 28

OK thanks you really are a Hero!! :) thanks for your help too Radar!

Answer 29

last question that would make it the second to last answer, right?

Answer 30

@StudyGirl21, I believe you have enough information to figure out what the answer is on your own.

Answer 31

OK, I'll go with the second to last one, thanks! :)

Answer 32

Yes, you see the x term dropped out in the process of attempting a solution by the substitution method.

Answer 33

Thanks you two!! :)

Answer 34

You're welcome and good luck in your studies. Love the profile.

Answer 35

thanks! Bye! :)