Hei! :)
[tex]\left \{ {{5x=2y} \atop {x*y=10}} \right. <=>\left \{ {{5x-2y=0} \atop {x=\frac{10}{y} }} \right. \\=> 5*\frac{10}{y}-2y=0/*y\\=> 50-2y^{2} =0\\-2y^{2}=-50 => y^{2}=+/-25 => y_{1}=5,\ y_{2} =-5\\\\=> x_{1} =\frac{10}{5} =2\\=> x_{2} =\frac{10}{-5} =-2\\\\=> ( x_{1}, y_{1})=(2,5)\\=> (x_{2}, y_{2})=(-2, -5)\\[/tex]
