Question

The table below shows four systems of equations:


(System 1) 4x − 5y = 2
3x − y = 8

(System 2) 4x − 5y = 2
10x − 7y = 18

(System 3) 4x − 5y = 2
3x − 8y = 4

(System 4) 4x − 5y = 2
10x + 3y = 15

Which pair of systems will have the same solution?

A.) System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1
B.) System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2
C.) System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to three times the second equation in system 1
D.) System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to three times the second equation in system 2

Answer 1

help? @BeautifulMystery. @mathwizzard3 @parker.goodbar @pooja195 @readergirl12

Answer 2

@Nefxrious What is so hard about this?

You can just test all the answers out

Answer 3

@Needhelpstudying I tried but I don't understand what they are telling me

Answer 4

@Nefxrious Alright, hold on for a bit, @mathmale is helping me with another question. I'll help you in a bit.

Answer 5

@Needhelpstudying ok!

Answer 6

Hello, Neffy. Pairs of different equations can sometimes have the same solution.

You may have to solve all four given systems of linear equations, fnding a solution for each.

Are any 2 of these four solutions the same? If so, you've answered this question.

Answer 7

I'm sorry, but need to attend to other things right now. I do urge you to solve all 4 systems of linear equations given you in this problem, and then compare the solutions to see whether or not any 2 are the same.

Answer 8

@Nefxrious do you know how to solve systems of equations?

Answer 9

@Photon336 Yes

Answer 10

Yeah, it's probably just easier to do what @mathmale said and just solve them one by one. we can start by working on the first one

Answer 11

@Photon336 I did that and I got all of them wrong except one but it isn't an answer

Answer 12

sometimes it's better to eliminate one variable and then combine the two equations rather than doing substitution.

to get rid of y multiply one by 3 the other by -5

3(4x − 5y = 2)
5(10x + 3y = 15)

then combine

12x-15y =6
50x+15y =75

62x = 81

x = 1.31~

4x-5y = 2

4(1.31)-5y = 2

5.24-5y = 2

y = 0.646

x = 1.31, y = 0.646

4x-5y = 2

4(1.31)-5(0.646) = 2.01

Answer 13

eliminating a variable method is sometimes easier than substitution.

Answer 14

@Photon336 how did you get
3(4x − 5y = 2)
5(10x + 3y = 15)?

Answer 15

so do you notice something? I wanted to get rid of y so i multiplied one equation by 3 and the other by 5 and heres what i got

12x-15y = 6
+ 50x+15y = 75

when I add the top and bottom notice something -15y and +15y cancel out. so we're left with

62x = 81

so I multiplied both the top and equation by those numbers.

Answer 16

@Photon336 where did you get 3 and 5 ?

Answer 17

@Nefxrious that wasn't in the problem originally I multiplied the equations by 3 and 5 so I could get rid of y when I combined them.

Answer 18

@Photon336 Oh okay! So I just need to do that for the other equations?

Answer 19

yeah, but that's just for that particular one think to yourself: what numbers would you need to multiply the equations by to eliminate a variable.

Answer 20

you get what I did right? @Nefxrious ?

Answer 21

@Photon336 Yeah! I get! My big problem was trying to cancel out the variable.

Answer 22

the point is canceling out the variables

Answer 23

try this one

4x − 5y = 2
3x − y = 8

Answer 24

ask yourself? what variable do you want to eliminate: pick one

Answer 25

Photon336 I want to eliminate y

Answer 26

okay so We can eliminate this by multiplying the bottom equation by -5

check this out see how this goes.

TOP 4x-5y = 2
Bottom -5(3x-y = 8)

TOP 4x-5y = 2
BOTTOM -15x+5y = -40

notice when we add these two equations together -5y and +5y cancel out

Answer 27

@Photon336 then you would solve and get
-11x=-38
-11/-11x=-38/-11
x= 3.45

Answer 28

Then you can plug 3.45 = x back into the top one and you can get y

4x-5y = 2

Answer 29

@Photon336
4(3.45)-5y=2
13.8-5y=2
13.8-13.8-5y=2-13.8
5y/5=-11.8/5
y=-2.36

Answer 30

Yes nice job y = +2.36 not -2.36 x = 3.45 for this one.

Answer 31

@Photon336 why not negative? I plugged it in and I got 2.

Answer 32

I did it like this

13.8-2 = 11.8/5y = 2.36


let's check our answers they have to satisfy both the equations or else we're wrong.

x = 3.45, y =2.36


4x − 5y = 2

4(3.45)-5(2.36) = 2 correct

3(3.45) − 2.36 = 8 correct

we find that these two answers are correct b/c we plugged them into the top and bottom equations and got the answers we were supposed to get here.

Answer 33

@Photon336 okay I made the 11.8 a negative

Answer 34

hm, okay but for me i just hate using negative numbers lol so when i can i try to make everything positive

Answer 35

@Photon336
when it looks like this
4x-5y=2
10x-7y=18
would you do
-7(4x-5y=2)
5(10x-7y=18)?

Answer 36

Yep you're getting the hang of it when you add those together you'll get -35y and +35y