Question

Solve the following system of equations.
7x+2y=5
2x+3y+16

Answer 1

There is a couple of ways to go about this
Which way(s) do you know?

Answer 2

we can do elimination or substitution?

Answer 3

i have no idea

Answer 4

what?

Answer 5

7x+2y=5 ---- (1)
2x+3y+16=0
2x+3y=-16 ----(2)
now u understand?

Answer 6

Oh wait you are missing an equal sign in the second *equation*

Answer 7

oh you're right!

Answer 8

7x+2y=5
2x+3y=16

Answer 9

So I was saying thre is two ways
And I was asking what way of the two ways I mention do you prefer?
(Note I do not recommend graphing to solve a system of liner equations because sometimes it ends up being an approximation)

Answer 10

I think aamal was talking about the elimination way :)

Answer 11

I'm correct to say she?
We want to add the equations together such that one of the variables zeros out when doing so
Do you know an equation still holds if you multiply both sides by the same thing?

Answer 12

Like I like to work with the small numbers
Look at the coefficients of y in both equations
Can you tell me what they are?

Answer 13

2 and 3?

Answer 14

yes exactly
What do you get when you multiply those numbers?

Answer 15

6

Answer 16

So is there a number we can multiply the first equation by such that the coefficient of y in the first equation is 6?

Answer 17

You told me 2(3)=6 right?

Answer 18

yes i did

Answer 19

ok great!
So if we multiply the first equation by 3 we will get the coefficient of y in the first equation to be 6
like so
21x+6y=15
Do you see how everything in the first equation got multiplied by 3?

Answer 20

yes i do see that

Answer 21

Do you know what we will multiply the second equation by?
Remember we are trying to get both y's to have coefficient 6.

Answer 22

2?

Answer 23

yes! :)
so what would the second equation look like?

Answer 24

\[2(2x+3y=16)\]
is that right?!

Answer 25

yes

Answer 26

So....
that would be what after distributing the two?

Answer 27

i honestly don't know

Answer 28

Ok so when I multiplied everything in the first equation by 3 this is what I did:
3(7x+2y=5)
3(7x+2y)=3(5)
3(7x)+3(2y)=3(5)
3(7)x+3(2)y=3(5)
21x+6y=15
I multiplied each term by 3
--------
So you wrote that we need to do
2(2x+3y=16)
2(2x+3y)=2(16)
2(2x)+2(3y)=2(16)
Can you finish this part?

Answer 29

\[4x+6y=16\]

Answer 30

well almost 2(16)=32 right?

Answer 31

oh yes!

Answer 32

So we have the two equations rewritten as:
21x+6y=15
4x+6y=32

right?

Answer 33

yes

Answer 34

Now all you do is take the opposite of one of these equations (it doesn't matter which but just do one)
What I mean by opposite is that we will just change the sign in front of each term...
This will elimination the y terms when we add the equations together

Answer 35

Do you know what I mean?

Answer 36

yes i know what you mean so it will now look like \[-4x-6y=-32\] am i right?

Answer 37

So the opposite of (4x+6y=32) is -4x-6y=-32
And like I said just do this for one of the equations (NOT BOTH and it doesn't matter which you choose)
omg perfect!
that is the exact equation I used lol

Answer 38

Now lets add these monsters!

Answer 39

wait why would you add?!

Answer 40

So first let me just write what we have
21x+6y=15
-4x-6y=-32
-------------

When you add these it will eliminate the y term

Like we will add the x terms 21x-4x=17x
We will add the y terms 6y-6y=0y=0
We will add the constants (that is the number that is not being multiplied by a variable)
15-32=-17

---------
So we have

21x+6y=15
-4x-6y=-32
-------------
17x =-17

Do you see what I mean?

Answer 41

oh yeah i see now!

Answer 42

So now we are trying to solve 17x=-17
Do you know how to solve this?

Answer 43

divide by 17 on both sides

Answer 44

Yes great! :)

Answer 45

which =-1

Answer 46

yes x is -1 ! :)

Answer 47

so x=-1 ?!

Answer 48

yayy! thank you so much!

Answer 49

Now .... we are almost done....

Answer 50

We need to solve for y

Answer 51

Can you do that?
Since we know x is -1 then we should be able to replace x with -1 in either equation which will mean we will only have one unknown in that equation which is a very good thing....

Answer 52

So we had 7x+2y=5 as one of the equations
...
We know x is -1 so we will replace x with -1
like so
7(-1)+2y=5

Answer 53

You could have chose either equation you started out with, it doesn't matter. Just use one though. All you need is one. You can do both but that is extra work.

Answer 54

Do you see that we only have one unknown in the equation 7(-1)+2y=5?

Answer 55

yes i do

Answer 56

Ok do you know how to solve this for y?

Answer 57

no i don't know

Answer 58

Go ahead and apply order of operations to the left hand side of the equal sign
Like multiplication comes first out of the operations given in the left hand side
So we do 7 times -1 which is -7
So we have
-7+2y=5
right?

Maybe this looks better to you...?

Answer 59

yeah i did that!

Answer 60

Now you can't add -7 and 2y because -7 and 2y are not liker terms so you have done all you could to that one side

Answer 61

Great! :)

Answer 62

So we have -7+2y=5
And we want to isolate the y
So we must figure out some way to undo the operations around the y to get it by itself
Now remember whatever you do to one side of the equation you must do to the other

Answer 63

So I usually like to undo additions and subtractions before undoing the multiplication and divisions

Answer 64

add the -7 to 5

Answer 65

Well add 7 on both sides (not -7)

Do you know what we want to add 7 on both sides and not -7?

Answer 66

why*

Answer 67

wouldn't y=6?!

Answer 68

yep :)
You did it!
Go you! :)

Answer 69

thanks so much! you really helped me to understand and especially because i have my algebra exams on thursday i know im going to need to know this!

Answer 70

Good luck! Practice practice! :)

Answer 71

i will! and thanks :)