Question

solve the system of following equations 1/2(2x+3y) +12/7(3x-2y)=1/2 and 7/2x+3y+4/3x-2y=2​

Answer 1

1/2(2x+3y)+12/7(3x–2y)=1/2

7/(2x+3y)+4/(3x–2y)=2

Let 1/(2x+3y)= u & 1/(3x-2y)= v

Then the given system of equations becomes

u/2 + 12v/7= 1/2

(7u + 12×2v) / 14= 1/2

(7u + 24v) =( ½) × 14

7u +24v = 7……………..(1)

7u + 4v = 2 ………………(2)

Subtracting equation 2 from eq 1.

7u +24v = 7

7u + 4v = 2   [elimination method]

(-)  (-)     (-)

--------------------

20 v = 5

v = 5/20= ¼

Putting v = ¼ in equation 1.

7u +24v = 7

7u + 24 (¼) = 7

7u + 6= 7

7u = 7-6

7u = 1

u = 1/7

Now,

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

(2x+3y) = 7……………(3)

v = ¼ = 1/(3x-2y)

(3x-2y) = 4……………..(4)

Multiply equation 3 by 2 an equation 4 by 3,

4x + 6y = 14……………(5)

9x - 6y =12……………..(6)

Adding Equations 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 = 14 -8

6y = 6

y = 6/6= 1

y = 1

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

Plz mark as brain list.