Question

Solve by elimination: 3x+4y=1
5x-3y=21
please help.

Answer 1

you can eliminate x, or y

which one do you want to eliminate?

Answer 2

ok lets eliminate y

Answer 3

to be able to eliminate the variables must be in the same magnitude

Answer 4

4y

3y

so, we need the least common multiple

Answer 5

2?

Answer 6

Or 1

Answer 7

4 and 3

what is it called .... both can get a number when multiplied
we want the smallest one. which one is it ?

Answer 8

It's 1

Answer 9

we need as if it was LCD least common denominator

Answer 10

same problem

Answer 11

from 3 and 4

Answer 12

so we can multiply both terms
with any number

and then they must be the same

Answer 13

3x+4y=1 5x-3y=21

Answer 14

So 1 wouldn't be the least Lcd?

Answer 15

no, 3 and 4 are different!

Answer 16

3*1 is not equal to 4*1

Answer 17

This is where I get confused
Ohhhh I see what you're saying now

Answer 18

yeah, I don't know what its called!!!
but it works like here\[\frac{ 1 }{ 3 } ,\frac{ 1}{ 4 }\]

Answer 19

Ohh I see now, now it's making sense lol.

Answer 20

:)

Answer 21

so the smallest common one is 12 I believe

Answer 22

the 3 fraction needs to be extended by 4,

and the 4 fraction by 3.

Answer 23

we have equations here, not fractions, but it works very similar:

3x+4y=1
5x-3y=21

the above one has 4y. we need to extend the equation by 3

the below one has -3y, so a 3 term. we need to extend eq by 4

Answer 24

we do this, so that the y terms are then the same type of y term
(same number with y)

Answer 25

9x+12y=3 <- was multiplied by 3
20x-12y=84 <- was multiplied by 4

Answer 26

Okay, A bit complicated but I'm getting it, there we go. I was about to ask where do we multiply those terms

Answer 27

But that's not it right?

Answer 28

now we add them together :) that's the "elimination " part:

9x+12y=3
+ 20x-12y=84
-------------
29 x = 87

the y was actually "eliminated" when adding, because it was once
positive once negative, with same magnitude

Answer 29

This make's sense. It's like how my teacher did it but I didn't know it was being eliminated when adding

Answer 30

So how do we get the x, and y from here?

Answer 31

we have 29 x

29 x = 87

well we want x, so we should divide both sides by 29

Answer 32

which gives us 3

Answer 33

yep

and then, you can plug that in any of the two original equations
and solve for y, to also have that

Answer 34

Thanks so much, I really needed this

Answer 35

glad we figured it out :)

Answer 36

Wait, now one sec lol. So when I solve for y it's the exact same thing?

Answer 37

He left me lol, I'm still a bit confused.

Answer 38

Please help? lol .

Answer 39

3x + 4y = 1 ------- [1]
5x - 3y = 21 -------[2]

[1] x 5 ---- 15x + 20y = 5 ---- [3]
[2] x 3 ---- 15x - 9y = 63 ----- [4]

[3] - [4] ----- 20y + 9y = 5 - 63
29y = -58
y = -2

substitute y= -2 in 1
3x + 4y = 1
3x - 8 = 1
3x = 9
x = 3

x= 3
y= -2

Answer 40

I love you so much. lol.

Answer 41

i love it as you undertand.... and give a medal..lol