Question

1/2(2x+3y)+12/7(3x-2y)=1/2​

Answer 1

Answer:

solution

1/2(2x+3y)+12/7(3x-2y)=1/2

7/(2x+3y)+4/(3x-2y)=2

let 1/(2x+3y)=U and 1/ (3x-2y)=V

=U/2+12V/7=1/2

(7U+12*2V) /14=1/2

(7U+24V)=(1/2)*14

7U+24V=7___(1)

7U+4V=2..........(2)

subtracting equation 2 form eq.1

7U+24V=7

7U+4V=2 [elimination method]

(-) (-) (-)

__________

20V=5

V=5/20

=1/4

putting v = 1/4 in equation 1.

7u+24v=7

7u+24 (1/4)=7

7u+6=7

7u=7-6

7u=1

u=1/7

now

u=1/7=1/(2x+3y)

(2x+3y) =7.......... (3)

v= 1/4=1/(3x-2y)

(3x-2y)=4......... (4)

multiply equation 3by 2 an equation 4 by 3

4x+6y=14...........(5)

9x-6y=12...........(6)

adding equation 5 and 6

4x-6y=14

9x-6y=12

13x=26

x=26/13

x=2

putting x= 2 in question 5

4x+6y=14

4 (2) +6y=14

8+6y=14

6y=6

y=6/6=1

y=1

Hence x= 2, y =1 is the solution of the given system of eqution