Question

Solution of 2/x+3/y=13 and 5/x-4/y=-2

Answer 1

Let 1/x be u and 1/y be v.

Then, 2u + 3v = 13 __(1)

and, 5u - 4v = - 2 __(2)

______________________________

By multiplying 5 × (1) and 2 × (5),

→ 10u + 15v = 65 __(3)

→ 10u - 8v = - 4 __(4)

______________________________

By subtracting (3) by (4),

→ 23v = 69

→ v = 3

______________________________

By susbtituting value of v in (1),

→ 2u + 3v = 13

→ 2u + 3(3) = 13

→ u = 4/2

→ u = 2

Therefore x = 1/2 and y = 1/3.