Question

Solve the following systems of equations.
$\frac{x}{y}+\frac{y}{x}=\frac{13}{6},x+y=5$

Answer 1

Given equations,

$x+y=5$

$\frac{x}{y}+\frac{y}{x}=\frac{13}{6}$

$6x^2+6y^2=13xy$

$6x^2-13xy+6y^2=0$

$(2x-3y)(3x-2y)=0$

$2x=3y$ (or) $3x=2y$

$2x=3y$, $x+y=5$

$\frac{5y}{2}=5$

$y=2,x=3$

$3x=2y$ , $x+y=5$

$\frac{5y}{3}=5$

$y=3,x=2$

$(x=2,y=3)$ and $(x=3,y=2)$ are solutions of given equations