how to solve ?2x+3y=12&4x-5y=15?

2x+3y=12---------multiplying the equation with 2
4x-5y=15

=>4x +6y = 24
4x-5y=15
---------------
11y=9 =>y= 0.81
---------------

substitute y value in ist equation...

2x+3(0.81) =12

2x+2.43=12

2x=9.57

x=4.78

so,
~~~~~~~~~~~~~~~~~~~~~~~~
x=4.78 and y= 0.81
~~~~~~~~~~~~~~~~~~~~~~~

solve for one variable first. (either x or y) and then substitute. if you solve for x: subtract 5y from the left and right. divide both sides by -2x. you get x= (15-5y)/-2 now that you know what x equals, plug that into the equation wherever x is. now you have -2((15-5y)/-2) + 5y = 15 once you solve this for y, you have the values of both variables.

10x + 15y = 60
12x - 15y = 45------ADD

22x = 105
x = 105 / 22

105/11 + 3y = 12
3y = 12 - 105/11
3y = 132/11 - 105/11
3y = 27/11
y = 9/11

x = 105/22 , y = 9/11

2x + 3y = 12
2x = 12 - 3y
4x = 2(12 - 3y)

4x - 5y = 15
2(12 - 3y) - 5y = 15
24 - 6y - 5y = 15
-11y = 15 - 24
-11y = -9
y = 9/11

2x + 3y = 12
2x + 3(9/11) = 12
2x = 12 - 27/11
2x = 132/11 - 27/11
2x = 105/11
x = (105/11)/2
x = 105/22

∴ x = 105/22 , y = 9/11

2x+ 3y=12
4x-5y=15
By elimination method,
multiply the eq. by 4 & 2

8x+12y=48
8x-10y=30
- + -
--------------------------
22y=18
y=18/22
y=9/11
put value of y in any of the above eq.

2x+3*9/11=12
2x=12-27/11
2x= 105/11
x=105/22
x=4.77
Ans---- x= 4.77
y=.82

yes, y nt? see this patiently:
u hav 2 equations: 2x + 3y = 12
4x - 5y = 15
1st, to make d co-efficients of x equal, multiply d 1st equation by 2. so, dis will b : 4x + 6y = 24
now, subtract d 2nd equation from d 1st one.
4x + 6y = 24 - (4x - 5y = 15)
u will get: y = 9/11 (4x will b cancelled out)
put this in eqn 1 n get x .
note: change d signs of eqn 2 wile subtracting.

x=4.7727
y=0.8182

(A) 2x+3y = 12
(B) 4x-5y = 15

Use 2 x (A) to get (C) 4x+6y = 24

(B) 4x-5y = 15
(C) 4x+6y = 24

(C)-(B) gives 4x-4x+6y-(-5y) = 24-15

=> 11y = 9
=> y = 9/11

Then substitute this into one of the equations, let's use (A) as it's the simplest:

(A) 2x+3(9/11) = 12

=> 2x+ (27/11) = 12
=> 2x = 12-(27/11) = (132/11) - (27/11) = 105/11
=> x = 105/22

Therefore x=(105/22), y=9/11.

If you're really good, you'll check your answer by substitution:

Try (B):

4x-5y = 15?

4(105/22) - 5(9/11) = (210/11) - (45/11) = 165/11 = 15

Hey, it works!

Then you know it's right. Use this method every time and you can't go wrong.

(2x+3y=12)*2
4x+6y=24
4x-5y=15
- + -
---------------
11y=9
y=9/11

2x+3y=12
2x+3*9/11=12
2x+27/11=12
2x=12-27/11
x= (12-27/11)/2= 5.590

Multiply the first equation by 2 then u'll get :
4x + 6y = 24
now subtract 2nd eq from this eq.
11y = 9
=> y = 9/11
Now substitute this value in any eq to get value of x.
2x + 3(9/11) =12
=> 2x + 27/11 =12
=> 2x = 12- 27/11 =105/11
=> x = 105/22