Question

1/2 (3x+4y)+1/5 (2x-3y)=1/4,5/(3x+4y)-2/(2x-3y)=3/2

Answer 1

Let (3x + 4y) = P and (2x - 3y) = Q
Then, 1/2P + 1/5Q = 1/4
10/P + 4/Q = 5 ------(1)
Similarly, 5/P - 2/Q = 3/2 ------(2)

2 × equation (2) + equation (1)
2(5/P - 2/Q ) + (10/P + 4/Q) = 3/2 × 2 + 5
⇒10/P + 10/P = 8
⇒ 1/P = 2/5 ⇒P = 5/2 put it in equation (2)
10/(5/2) + 4/Q = 5
⇒ Q = 4

Now, P = (3x + 4y) = 5/2 ⇒6x + 8y = 5
Q = (2x - 3y) = 4

(6x + 8y) - 3 × (2x - 3y) = 5 - 3 × 4
⇒6x + 8y - 6x + 9y = 5 - 12
⇒17y = -7 ⇒y = -7/17

And x = (4 + 3y)/2 = (4 - 21/17)/2 = (68 - 21)/34 = 47/34