Question

Use the elimination method to solve the system of equations. Choose the correct ordered pair.

6x + 5y = 61
-5x + 5y = -5

A. (6, 3)
B. (6, 5)
C. (8, 3)
D. (8, 5)

Answer 1

@ShadowLegendX could you help me?

Answer 2

Hey @Tallan

Answer 3

Could you help me out with this problem??

Answer 4

Ok, do you remember how I taught you substitution a couple days ago? This is similar

Answer 5

Yes, I remember it a little bit.

Answer 6

6x + 5y = 61
-5x + 5y = -5

Multiply 6x + 5y = 61 by 5

Multiply -5x + 5y = -5 by 6

30x + 25y = 305
-30x + 30y = -30

Eliminate

25y = 305
30y = -30

Add

55y = 275

Divide both sides by 5

y = 5

Answer 7

Now this next step is similar to what we did in that other systems of equations that we did. What do you think the next step is @Tallan ?

Answer 8

Divide?

Answer 9

Umm no.

We already solved for y

y = 5

Answer 10

ohh right sorry then we divide for 6x and -5x?

Answer 11

Divide? Why would we divide for 6x and -5x o-o

Answer 12

idk..

Answer 13

@Tallan I really want you to get this concept so you will be able to do it on your own.

6x + 5y = 61
-5x + 5y = -5

When solving for a system of equations, we are looking for for two points, for the two variables x and y. We just solved for that variable y, but what next after that?

Answer 14

would we add?

Answer 15

Why would we add?

Answer 16

@Tallan I'm trying to understand your thought process here so I can teach you better

Answer 17

cause you want to get rid of the negative?

Answer 18

I am not asking for the next step as in, we're going to divide or add. But what is our next purpose in this system of equations. We already solved for y, but what else is there to be solved for?

Answer 19

solve for x

Answer 20

YES!!!!!!!!!!!!!!!!!!

Answer 21

Once you solve for one variable in a system of equations, you look to the other variable, which in this case is x

Answer 22

Would we have to multiply to find that answer to?

Answer 23

Now, we are going to try solve for x. Since you are new and just learning the concept, I'll choose the easier one of the two equations for this.

-5x + 5y = -5

What do we do with y?

Answer 24

Remember, y = 5

Answer 25

5*5

Answer 26

-5x+5*5=-5

Answer 27

You're correct, but I want you to think of it this way.

You're inputting in 5 for y. "Substituting"

That's why I find elimination funny as half of it is just using substitution xD

Answer 28

haha

Answer 29

But yes, you're correct.

-5x +5(5) = -5

Answer 30

I want you to try solve for that

Answer 31

Am I starting it right?
-5x +5(5) = -5
-5x +20=-5

Answer 32

Would it be B? @ShadowLegendX

Answer 33

Incorrect, 5 x 5 does not equal 25...

Answer 34

darn it i knew that i just pressed wrong key... I knew that .
5x5 = 25

Answer 35

@Tallan Are you able to multiply?

Answer 36

5 x 5 = 5 + 5 + 5 + 5 + 5

Five 5's

Answer 37

yes/..

Answer 38

So B is incorrect?

Answer 39

Well, how did you get B in the first place?

Answer 40

25/4..... to get 6.25 so i rounded down to 6.. I'm just trying to find the answers quickly.

Answer 41

I have no idea why you divided 25 by 4. Care to explain that part?

Answer 42

i am not quite sure. i just divided. xD

Answer 43

i honestly can't think straight.

Answer 44

@Tallan

When solving for a system of equations, we want to find the x and y points. We want to end up with something like

y = 8
and
x = 2

To do that, we have to solve/isolate for the variable.

Let me do a practice problem

3x = 15

Solve for x

Answer 45

@Tallan

Solve 3x = 15

Answer 46

it would be 5

Answer 47

3x5=15

Answer 48

But what step would you first do to get 5?

Answer 49

divide 3 to get x alone and divide 3 by 15

Answer 50

EXACTLY!!!

We want to get the variable alone

Answer 51

But to do that, we have to know when to divide, and divide by the correct numbers. Where you grabbed 4 earlier, I don't know, but lets continue

Answer 52

would x = 1?

Answer 53

Nope

Answer 54

darn...

Answer 55

Lets start off where we left

-5x +5(5) = -5

I believe you corrected your mistake of 5(5) not being 20, but being 25

So that means...

-5x + 25 = -5

What would you do now?

Answer 56

subtract 25 from both sides?

Answer 57

Yes!!!

Answer 58

Show me what you get

Answer 59

-5x=-30

Answer 60

Correct, so what would you do now?

Answer 61

-5/-5 -30/-5?

Answer 62

Yes, divide -5x by 5, and divide -30 by 5

What do you get now?

Answer 63

6

Answer 64

so it would be B

Answer 65

Btw, remember to keep x in your equation, next to -5

Answer 66

Tallan, that's correct :)

Answer 67

Now, remember when I taught you substitution, what did I tell you to do after you solved for both points?

Answer 68

check to make sure its right.

Answer 69

Yep

I want you to input both points into both equations to see if they come out correct :)

Answer 70

if you take 6 * 6 + 5y = 61 it comes out y=5

Answer 71

so it is right.

Answer 72

6(6) + 5(5) = 61

36 + 25 = 61

61 = 61

Correct

Answer 73

Check the other one

Points:
y = 5
x = 6

Answer 74

it comes out 4
-5*5+5y=-5 it came out 4

Answer 75

y=4?

Answer 76

-5x + 5y = -5

Answer 77

How did you get 4? Show me your work ^-^

Answer 78

nvm..
-5*5+5y=-5 it comes out to -20

Answer 79

i think i typed it wrong on the calcultor.

Answer 80

This is the same mistake as last time.

Answer 81

You think that 5 x 5 is 20

Answer 82

But it's not...It's 25

Answer 83

I know, but when i put the equation in my calcultor it came out -20.

Answer 84

Your calculator is incorrect then

-5(6) + 5(5) = -5

-30 + 25 = -5

-5 = -5

Answer 85

Btw I just noticed that you inputted in the wrong points for the wrong variables

Answer 86

oh i put that in wrong... thats why i got the wrong answer/.
but (6,5) Works..

Answer 87

Yes @Tallan B is correct. But I want you to get this concept down, as it is just basic algebra and there are much harder concepts

Answer 88

Believe i am sure there are.... I have 130 to do by the 23. i have to do 17 a day to get everything done on time.

Answer 89

Alright @ Tallan I'll be on here pretty much all day as today is a free day for me. Tag me when you need help but I may be afk sometimes, so if I can't make it, tag some of my friends like:

@camerondoherty
@sammixboo
@iambatman
@pooja195

Answer 90

Ok Just before i close this question do i have this in the right order?
Place the four steps of the elimination method in the proper order.



Find the variable with equal or opposite coefficients.

If equal, subtract the equations. If opposite, add the equations.

Solve the resulting one-variable equation.

Substitute the known value into the other equation and solve for the remaining variable.

Answer 91

Looks good

Answer 92

Sweet thanks!

Answer 93

3x - 4y = -30
3x + 2y = 6

would you still multiply for this equation?

Answer 94

??

Answer 95

nvm i figured it out.

Answer 96

You would multiply with the y section