Question

8/x-3/y=18/xy,5/x+4/y=23/xy​

Answer 1

Answer:

x = 2, y = 3

Step-by-step explanation:

$\frac{8}{x} - \frac{3}{y} = \frac{18}{xy} \\ \frac{8y - 3x}{xy} = \frac{18}{xy} \\ 8y - 3x = \frac{18 \times xy}{xy} = 18 \\ - 3x + 8y = 18 \\ \\ \frac{5}{x} + \frac{4}{y} = \frac{23}{xy} \\ \frac{5y + 4x}{xy} = \frac{23}{xy} \\ 4x + 5y = \frac{23 \times xy}{xy} = 23$

-3x + 8y = 18 ---(1)

4x + 5y = 23 ---(2)

Multiplying eq 1 by 4 and eq 2 by 3

-12x + 32y = 72 ---(3)

12x + 15y = 69 ---(4)

Adding eq 3 and 4,

47y = 141

y = 3

Substituting y = 3 in eq 1

-3x + 8×3 = 18

-3x + 24 = 18

-3x = -6

x = 2