Question

$\frac{22}{x+y}+\frac{15}{x-y}=5$
$\frac{55}{x+y}+\frac{45}{x-y}=14$

• A. $x=-8$, $y=3$
• B. $x=-3$, $y=8$
• C. $x=8$, $y=3$
• D. $x=8$, $y=-3$

Answer 1

Answer: (C)

$x=8$, $y=3$

$let\left(\frac{1}{x+y}\right)=uand\left(\frac{1}{x-y}\right)=vthen22u+165v=5\to \left(1.\right)and55+45v=14\to \left(2.\right)multiplyequation\left(1.\right)by3,weget66u+45v=15\to \left(1.\right)+55u+45v=14\to \left(2.\right)uponsubtractionof\left(1.\right)with\left(2.\right),weget11u+0=1\therefore u=\left(\frac{1}{11}\right)orx+y=11\to \left(3.\right)andthenv=\left(\frac{5-22u}{15}\right)=\left(\frac{5-2}{15}\right)=\left(\frac{1}{5}\right)\therefore x-y=5\to \left(4.\right)add\left(3.\right)and\left(4.\right)equationweget2x=16\therefore x=8andy=11-x=11-8=3$