Question

FAN AND MEDAL

System A -
-4x + 6y = -2
2x + y = 5

System B
-10x + 19y = -1
-4x + 6y = -2

Answer 1

Do you know how to do elimination?

Answer 2

Which of the following statements is correct about the two systems of equations?


They will have the same solutions because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

The value of x for System B will be –5 times the value of x for System A because the coefficient of x in the first equation of System B is –5 times the coefficient of x in the first equation of System A.

The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding –12 to the first equation of System A and the second equations are identical.

Answer 3

Sorry that took me so long, the connection was really slow /:

Answer 4

I think in order to answer that you need to solve the systems.

Answer 5

I don't really know how to do that..
I've had a hard time with this.

Answer 6

In order to solve by elimination, you want to multiply one equation by some number so that one of the variables cancels out. Let's look at system A first and eliminate x. What should we multiply the second equation by so that, when you add the two equations, the x cancels itself out?

Answer 7

I'm not sure, I'm sorry ugh.
I'm good at algebra it's just for some reason this is extremely difficult for me.
I don't want to waste your time!

Answer 8

You're not wasting my time if you are willing to learn.
What do you need to add to -4x to make 0?

Answer 9

Thank you so much you have no idea.

4? But you can't add 4 to -4x because 4 doesn't have x also right?

Answer 10

What about 4x?

Answer 11

Yes.
So then with the second equation would you subtract 2x ?

Answer 12

No. What do you need to multiply 2x by to make 4x?

Answer 13

2x ?

Answer 14

no, just 2. So, if we multiply all of the second line by 2, we get
4x+2y=10

now, we add the two equations together:

So we get 8y=8. That makes y= ?

Answer 15

1 ?

Answer 16

because you divide by 8 on both sides to get y alone right?

Answer 17

exactly. Now, we have to plug in that value of y into one of the equations in system A to find x.

Answer 18

So if I did the first equation, Would it be -4x + 6 = -2 ?
So solving that you would get x = 2 ?

Answer 19

perfect. So your solution for system A is (2, 1)

Answer 20

Now, for system B: What should we multiply the second equation by to eliminate x when we add it together?

Answer 21

^ actually we will need to multiply both equations here.

Answer 22

4x right?

Answer 23

But for the first equation in system B wouldn't you add 10 ?

Answer 24

We'll try to make -20x on top, so we multiply the top equation by ??
We'll try to make +20x on bottom, so we multiply the bottom equation by ??

Answer 25

No wait that was wrong .
Ugh I don't know.

So we'll multiply the top equation by 2 ?
And we'll multiply the bottom by 5 ?

Answer 26

bottom by -5 (you have -4,so we want to cancel out the negative). But good job otherwise.
So when we multiply each term by those, what are our new equations?

Answer 27

19y = -1
6y = -2 ?

Answer 28

Not quite. We are looking for:
2(-10x) + 2(19y) = 2(-1) AND
-5(-4x) - 5(6y) = -5(-2).
Can you simplify those?

Answer 29

I'm not sure..
I don't think so because you cant simplify x and y right ?

Answer 30

I meant multiply them out.

Answer 31

I don't know. I'm so sorry.

Answer 32

I'll do the first one...
-20x + 38y = -2
Seeing what I did, can you do the next one?

Answer 33

20x - 30y = 10?

Answer 34

perfect!
Now, doing the addition I did before, what do you get?

Answer 35

if I'm adding the 30y and the 38y would the 30y be negative because it was being subtracted ?

If so, the equation would be 8y = 8

So y = 1 again

Answer 36

Yep! Now, can you solve for x?

Answer 37

-10x + 19 = -1
-10x = -20
x = 2

Answer 38

Yes, and that matches what we have before (2,1).
Now going back to the 4 options, we have the same solution for both systems. So, which one is it?

Answer 39

The options are phrased weirdly.

Answer 40

A or B ?

Answer 41

I don't understand why they would do it the way they are, but B is right.