a) $\left \{ {{x+y=17} \atop {x.y=180}} \right.$
⇔ $\left \{ {{x=17-y} \atop {(17-y).y=180}} \right.$
⇔ $\left \{ {{x=17-y} \atop {17y-y^{2}=180}} \right.$
⇔ $\left \{ {{x=17-y} \atop {y^{2}-17y+180=0}} \right.$
⇔ $\left \{ {{x=17-y} \atop {y^{2}-2.y.\frac{17}{2}+\frac{289}{4}+180-\frac{289}{4}=0}} \right.$
⇔ $\left \{ {x=17-y \atop {(y-\frac{17}{2})^{2}+\frac{431}{4}=0 ( vô lí )}} \right.$
Vậy ko có giá trị x, y t/m ...
b) $\left \{ {{x^{2}+ y^{2}=61} \atop {xy=30}} \right.$
⇔ $\left \{ {{x^{2}+ y^{2}=61} \atop {2xy=60}} \right.$
⇔ $\left \{ {{x^{2}+ y^{2}-2xy=61-60=1} \atop {xy=30}} \right.$
⇔ $\left \{ {{(x-y)^{2}=1} \atop {xy=30}} \right.$
⇔ $\left \{ {{x-y=1} \atop {xy=30}} \right.$
⇔ $\left \{ {{x=y+1} \atop {(y+1).y=30}} \right.$
⇔ $\left \{ {{x=y+1} \atop {y^{2}+y-30=0}} \right.$
⇔ $\left \{ {{x=y+1} \atop {(y-5)(y+6)=0}} \right.$
⇔ $\left \{ {{x=y+1} \atop {\left[ \begin{array}{l}y=5\\y=-6\end{array} \right.}} \right.$
\(\left[ \begin{array}{l}\left \{ {{x=6} \atop {y=5}} \right.\\\left \{ {{x=-5} \atop {x=-6}} \right.\end{array} \right.\)
c) $\left \{ {{x-y=6} \atop {xy=40}} \right.$
⇔ $\left \{ {{x=y+6} \atop {(y+6).y=40}} \right.$
⇔ $\left \{ {{x=y+6} \atop { y^{2}+6y-40 =0}} \right.$
⇔ $\left \{ {{x=y+6} \atop {(y-4)(y+10)=0}} \right.$
⇔ $\left \{ {{x=y+6} \atop {\left[ \begin{array}{l}y=4\\y=-10\end{array} \right.}} \right.$
\(\left[ \begin{array}{l}\left \{ {{x=10} \atop {y=4}} \right.\\\left \{ {{x=-4} \atop {y=-10}} \right.\end{array} \right.\)