Question

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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]

(-)  (-)     (-)

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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

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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.

Answer 2

Answer:

x = 2

y = 1

Step-by-step explanation:

Let 1 / ( 2 x + 3 y ) be a

Let 1 / ( 3 x - 2 y ) be b

a / 2 + 12 b / 7 = 1 / 2

⇒ a + 24 b / 7 = 1

⇒ 7 a + 24 b = 7 .......( 1 )

Another equation is :

⇒ 7 a + 4 b = 2 .......( 2 )

Subtract 2 from 1

24 b - 4 b = 7 - 2

⇒ 20 b = 5

⇒ b = 5/20

⇒ b = 1/4

7 a + 1 = 2

⇒ 7 a = 1

⇒ a = 1/7

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

⇒ 2 x + 3 y = 7

Multiply by 3 :

6 x + 9 y =21

Also :

3 x - 2 y = 4

⇒ 6 x - 4 y = 8

Subtract that :

13 y = 13

= y = 1

3 x - 2 = 4

= 3 x = 6

= x = 2

Hence x = 2 , y = 1