Question

Solve for (x,y)
{X+2y=3
{2x+3y=3

Answer 1

As there are 2 equations! They will have 1 solution ONLY
So let us multiply the first equaition with 2 to get x co-eff. common okay?
It'll become = 2x + 4y = 6
Now subtract this equation by 2x + 3y = 3
So 2x + 4y - 2x - 3y = 6-3
so y would be?
And then substitute y's value in any of the above equations to get the x value and then you will get the point of there intersection
Understood? :)

Answer 2

Why do you multiply by 2 on the first step

Answer 3

There ARE actually many methods to do this!
You could have either found x value in terms of y and then you could have substituted that value of x in the second equation!
But in the multiplication method!
We should get the co-efficient of the variable x OR y [In this case 2 for x ]
Common so that when we subtract OR add the 2 equations IT GET'S CUT!!

Answer 4

For example in our case we could have also multiplied the first equation with 3 so that the y co-eff. in the first equation would become 6!
But then we would have had to multiply the 2nd equation also with 2 so that the y co-eff would become 6!
So that when we subtractted the 2 equations y would get CUT!! :-)

Answer 5

Getting the concept?

Answer 6

Yeah I got it. Thank you :)

Answer 7

Want to hhelp me with one more

Answer 8

Do you need help?

Answer 9

Yeah this other one is confusing

Answer 10

Kudos me? :)

Answer 11

{2x-3(y+1)=8
{3(x+2)+5y=-6

Answer 12

Okay so even in this case what you want to do is you've got to open the brackets for BOTH the equations using distributive property Al right?
Tell me what you get then!

Answer 13

I dont knowhow

Answer 14

So it goes like this
Say you have
-ax(bx - c)
Now how will you open the brackets here?

Answer 15

TRY TRY!! :D

Answer 16

{2x-3y+3=8
{3x+6+5y=-6

Answer 17

Second one is CORRECT but the first one should be 2x - 3y - 3!!
Getting why? :)

Answer 18

Yeah I forgot about the -

Answer 19

Okay so now 2x - 3y - 3 = 8 right?
Now bring the -3 to the RHS
it becomes 2x - 3y = 11
Do the same with the second equation now!

Answer 20

3x+5y=0

Answer 21

Then what?

Answer 22

No, the second one would become NEGATIVE when shifted there right?

Answer 23

Oh -12

Answer 24

Okay So do I subtract the two equations?

Answer 25

Hello?

Answer 26

Hold on

Answer 27

Okay so the 2 equations are?
2x - 3y = 11
3x+5y=-12
Now see for x and y!
Do you see the co-eff of x in both equations same?
Or do you see the co-effecient of y in both equations same?
YES/NO? :)

Answer 28

No?

Answer 29

Am I supposed to?

Answer 30

You are right IT IS NO!!
So that is why we MULTIPLY [*HURRAY*]

Answer 31

Do you understand what co-eff. means?

Answer 32

No

Answer 33

Okay so let us say we have ax
Now the co-efficient is like the constant attached to the variable
Okay?
So in here the( co-efficient of x) = a
Got that?

Answer 34

I think so

Answer 35

\[1x/2 , 4x/5 , c^2x\]
Find the co-efficients of these!
TRY! I'll help you

Answer 36

There are 3 of them okay?

Answer 37

Are they part of the problem

Answer 38

Not our problem!
I am trying to help you understand a very key part to solve your question!

Answer 39

Do you want to do the 3 I gave you or not?
Because I CAN tell you an easier way to solve your question!
But what I am showing you now is really very helpful!
YOUR CHOICE!

Answer 40

So it's like anything thats paired together that aren't the variables

Answer 41

YES!!! :D

Answer 42

K :)

Answer 43

let us get back to our question now

Answer 44

2x - 3y = 11
3x+5y=-12
Tell me the co-efficient of x in both the equations
Tell me the co-efficient of y in both the equations
[INCLUDE THE NEGATIVE SIGNS IF IT IS THERE]

Answer 45

2 and 3
3 and 5

Answer 46

Er...-3

Answer 47

Slightly wrong!
The co-eff. of y in the first equation is -3!!
Get it??

Answer 48

YES!!! :D

Answer 49

K so I multiply those

Answer 50

Now we have to make one of the variables' co-eff. SAME in both equations!
Getting me?

Answer 51

Yeah I got you but how do I do that

Answer 52

Good now let us say we want the co-eff. of x same in both the equations! okay?

Answer 53

K

Answer 54

So the co-eff of x
are
2
3
right?

Answer 55

Now we want them to be the same!
So we have to multiply them with some numbers that will fetch us similar numbers!
Do you know how to find LCM?

Answer 56

I think so. Can we pick up the pace a bit. I have school in 7 hours and still need to get to bed:/

Answer 57

Sure!
Now see if we have 2 and 3
We kinda need to find a number to multiply it with to get something common!
And that common number for the first equation is 3
And for the 2nd equation is 2!
So it is kinda like finding the LCM!
And when we multiply the equations accordingly we'd get 6x in both!
Okay?

Answer 58

K

Answer 59

Like this
3*(2x - 3y = 11) = 6x - 9y = 33
2*(3x+5y=-12) = 6x + 10y = -24
Now we do this because if we have something common in both equations then we can cut them off when we subtract them!

Answer 60

So coming back to your question!
{X+2y=3 --> multiply with 2 to get co-eff of x 2 in both cases!
{2x+3y=3 --> multiply with nothing because we already have the co=eff for x as 2!
And then subtract the 2 equations
Liek
2x + 4y - 2x - 3y = 6-3 (CHOP THE 2x off)
You get y=3
And then put the y value in the first equation [x + 2y = 3]
x + 2(3) = 3
x = -3
So the point will be (x,y) = (-3,3)
tHE ANSWER TO YOUR QUESTION!! :)
Getting me?? :D

Answer 61

@245424 ?

Answer 62

I got confusedt

Answer 63

Then do this easier thing!
X+2y=3 -> x = 3 -2y
{2x+3y=3
Now substitute x's value in the 2nd equation
as
2(3-2y) + 3y = 3!!
And now open the brackets and solve!
Getting that??

Answer 64

I think we messed up. My teacher gave us the answers. He got (-1,3)

Answer 65

Either you wrote the questionwrong!
Or your teacher was wrong!
Tell your teacher [TRY NOT TO BE DISRESPECTFUL]
THAT HE WAS WRONG!

Answer 66

Tell him IT IS (-3,3)

Answer 67

Oh well. He said as long as we tried he would give us credit. So I'll keep this work and just deal with it. Thank you vermouth for helping me

Answer 68

*very much

Answer 69

Best response maybe?? :!

Answer 70

Only RESPONSE maybe!! :P

Answer 71

How do I do that

Answer 72

Just press best response beside my answers!

Answer 73

Have fun in Math class!
Tell your sir to reCHECK!

Answer 74

K thanks :)

Answer 75

You're most wecome!