Question

solve by x and y :

$\frac{1}{2(2x + 3y)} + \frac{12}{7(3x - 2y)} = \frac{1}{2} \\ \\ \frac{7}{(2x + 3y)} + \frac{4}{(3x - 2y)} = 2$
where (2x + 3y )≠ 0.

Answer 1

Heya !!!

1/ 2 ( 2X + 3Y) + 12/ 7(3X -2Y) = 1/2 ----(1)

And,

7/ 2X + 3Y + 4/ (3X -2Y) = 2 --------(2)

Putting 1/ ( 2X + 3Y) = U and 1/ (3X - 2Y) = V. Then equation (1) and (2) becomes,

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

7U + 24V = 7 ----------(3)

And,

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

Subtract equation (2) from equation (1) we get,

7U + 24V = 7
7U + 4V = 2
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20V = 5

V = 5/20 => 1/4

Putting V = 1/4 in equation (1) we get,

7U + (24 × 1/4) = 7

=> 7U + 6 = 7

=> 7U = 7-6

=> 7U = 1

=> U = 1/7

Now,

1/2X + 3Y = U

1/2X + 3Y = 1/7

2X + 3Y = 7 ---------(4)

And,

1/ 3X - 2Y = V

1/ 3X - 2Y = 1/4

3X - 2Y = 4 ----------(5)

Multiply equation (4) by 2 and (5) 3 and add the result we get,

4X + 9X = 14 + 12

=> 13X = 26

=> X = 26/13

=> X = 2

Putting X = 2 in equation (4) we get,

(2X + 3Y) = 7

2 × 2 + 3Y= 7

4 + 3Y = 7

3Y = 7-4

3Y = 3

Y = 3/3 => 1



Hence,



X = 2 and Y = 1

HOPE IT WILL HELP YOU...... :-)

Answer 2

Hello dear user ...

Answer is given above attachment

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Hope it's helps you.
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