Question

x+y= 5 xy. 3x + 2y = 13 xy​

Answer 1

Answer:

$x = \frac{1}{2} \\ y = \frac{1}{3}$

Step-by-step explanation:

$x + y = 5xy \\ 3x + 2y = 13xy \\ \div by \: xy \: \\ \frac{x}{xy} + \frac{y}{xy} = \frac{5xy}{xy} \\ \frac{1}{x} + \frac{1}{y} = 5 \\ \frac{3x}{xy} + \frac{2y}{xy} = \frac{13xy}{xy} \\ \frac{2}{x} + \frac{3}{y} = 13 \\ let \: us \: take \: \frac{1}{x} = a \: and \: \frac{1}{y} = b \\ a + b = 5 - - - - eq1 \times 2 \\ 2a + 3b = 13 - - - - - eq2 \\ 2a + 2b = 10 \\ 2a + 3b = 13 \\ - b = - 3 \\ b = 3 \\ a + b = 5 \\ a + 3 = 5 \\ a = 2 \\ x = \frac{1}{2} \\ y = \frac{1}{3}$