Question

result of multiplication and addition to eliminate a variable in the system of equations? Of "2x + 3y = 6" and "5x + 2y = 4"

Answer 1

@terenzreignz:

Answer 2

Of course... Okay, so you need to pick a variable to eliminate... which one do you want to get rid of first? :)
(In this case, it doesn't really matter which)

Answer 3

x?

Answer 4

Okay, so, What do you multiply to 2 so that you get 5?

Answer 5

You can't multiply 2 by anything to get 5 unless its a decimal.

Answer 6

Okay, let's try another tack... what is the Least Common multiple of 2 and 5 (the coefficients of x in the equations)

Answer 7

10.......?

Answer 8

Okay, good :)
So what do you multiply to 2 to get 10?
What do you multiply to 5 to get 10?

Answer 9

We have
\[2x+3y=6\]
\[5x+2y=4\]
We want to get rid of the x, so what I would do is is multiply the top by -5 and the bottom by 2.
As such we would have

\[-10x-15y=-30\]
\[10x+4y=8\]

Answer 10

you multipy 2 x 5 to get 10 and 5 x 2 to get 10

Answer 11

Sorry, I just kinda jumped, but I already had it written....

Answer 12

Hahah it's okay.

Answer 13

Okay, so what I want you to do is multiply the first equation (the one with the 2x) with -5
and the second equation by 2....

Answer 14

How would I do that?

Answer 15

Like use " (,)" ?

Answer 16

And Distribute?

Answer 17

For instance, multiplying -5 to the first equation, we get:
-10x - 15y = -30

Answer 18

THen for the other equation I would get 10x=4y=8?

Answer 19

YOu mean 10x + 4y = 8, right? :P

Answer 20

Ohh yeah haha.

Answer 21

Okay, so recap... we now have
-10x - 15y = -30
10 x + 4y = 8

Now you can just add these equations together (What this means is form a new equation where the left side is the sum of the left-sides and the right, likewise)

Answer 22

So I'd have -10x-15y+10x+4y=8-30.....

Answer 23

mhmm :)
You'll notice that the x would... cancel out... (get eliminated)

Answer 24

Oh!

Answer 25

So.. simplify the equation, the x would cancel out, and you can simply solve for y :)

Answer 26

So far I have -15y+4y=8-30=10-10

Answer 27

Is that right?

Answer 28

-15y + 4y = 8 - 30
Solve for y.

Answer 29

Ohh I take out the 10's?

Answer 30

They disappear... they disappear, remember? Because they cancelled out :P

Answer 31

I'm sorry I'm really stupid I swear i'm not blonde.

Answer 32

:)
Just do it :D

Answer 33

I got y+y= 8-30+15-4..

Answer 34

You don't do that :D
You add similar terms...

Answer 35

What is that....

Answer 36

-15y + 4y = -11y :P
This is basic stuff D:

Answer 37

I'm sorry!!!! D:

Answer 38

so you get
-11y = -30+8
Simplify the right side?

Answer 39

Wait so I subtracted -15 and 4 and kept the 1 y?

Answer 40

Yes :P
think of it this way... we factored out the y:
\[\large -15y + 4y = y(-15+4)=y\cdot -11 = -11y\]

Answer 41

OHhh okay well how did I go from subtracting 30 to adding 30?

Answer 42

huh?

Answer 43

you put -11y= 8+30 when before it was -30 because it was a negative from multiplying -5 and 6.

Answer 44

NO.... I never put up 8+30
it's 8 - 30 :P
look again :D

Answer 45

Ohh sorry haha.

Answer 46

Okay, so we have
-11y = 8 - 30

Simplify /solve?

Answer 47

So I got -11y=-22 then I divided -22 by -11 and got positive 2 so y=2

Answer 48

Is that right!? :D

Answer 49

yes, y = 2 :)
Now replace y with 2 in any of the two equations you started with and solve for x.