Question

If 2/x+3/y=10 and 3/x+2/y=5, then find 1/x+1/y = ______ . a) 3 b)2 c) 4 d) 1/3​

Answer 1

Answer:

$\frac{\frac{2}{x+3}}{y} =10\\\\\frac{2}{y(x+3)} =10\\\\\frac{2}{yx+3y} =10\\\\2=10(xy+3y)\\\\2=10xy+30y\\\\1=5xy+15y$ equation 1

$\frac{\frac{3}{x+2}}{y} =5\\\\\frac{3}{y(x+2)} =5\\\\\frac{3}{xy+2y} =5\\\\3=5(xy+2y)\\\\3=5xy+10y$   equation 2

Subtract equation 1 and equation 2

$- 5xy+15y=1\\\\\\frac{-5xy+10y=3}{}$

0+25y=3

$y=\frac{4}{25}$

$3=5xy+10y\\\\3=5x*\frac{4}{25} +10*\frac{4}{25} \\\\3=x*\frac{4}{5} +2*\frac{4}{5} \\\\3=\frac{4x}{5} +\frac{8}{5} \\\\3=\frac{4x+8}{5} \\\\15=4x+8\\\\7=4x\\\\x=\frac{7}{4}$

$\frac{\frac{1}{x+1}}{y} \\\\\frac{1}{y(x+1)} \\\\\frac{1}{yx+y}$

Substituting the values

$\frac{1}{\frac{7}{4}* \frac{4}{25} + \frac{4}{25}} \\\\\\\LCM\\\frac{1}{\frac{28}{100} + \frac{4}{25}\frac{4}{4} } \\\\\\frac{1}{\frac{28}{100} + \frac{16}{100}} \\\\\\frac{1}{\frac{28+16}{100}} \\\\\\frac{100}{44} \\\\\frac{25}{11}$