Question

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solve step by step​

Answer 1

Answer:

let

1/(2x + 3y) = a

1/(3x - 2y) = b

a/2 + 12b/7 = 1/2......(1)

7a + 4b = 2.............(2)

(1) x 14 - (2) x 6

7a + 24b = 7

42a + 24b = 12

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

-35a = -5

a = 1/7

from (2)

7a + 4b = 2

7*1/7 + 4b. = 2

1 + 4b = 2

4b = 2 - 1

4b = 1

b = 1/4

now,

a = 1/7

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

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

b = 1/4

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

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

(3) x 2 + (4) x 3

4x + 6y = 14

9x - 6y = 12

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

13x =. 26

x = 2

from (3)

2x + 3y = 7

4 + 3y = 7

3y = 3

y = 1

so, solutions are

x = 2, y = 1