Question

Solve for x and y : x + y = 17, x² + y² = 169

Answer 1

$$\begin{gathered} x+y=17 \\ \Rightarrow x=17-y...\left(\mathrm{i}\right) \\ {x}^2+y^2=169...\left(\mathrm{ii}\right) \\ \mathrm{Substituting}\left(\mathrm{i}\right)\mathrm{in}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ {\left(17-y\right)}^2+y^2=169 \\ \Rightarrow 289+y^2-34y+y^2=169 \\ \Rightarrow 2y^2-34y+120=0 \\ \Rightarrow y^2-17y+60=0 \\ \Rightarrow y^2-12y-5y+60=0 \\ \Rightarrow y\left(y-12\right)-5\left(y-12\right)=0 \\ \Rightarrow \left(y-5\right)\left(y-12\right)=0 \\ \therefore y=5ory=12 \\ \mathrm{When}y=5, \\ x=17-5 \\ \therefore x=12 \\ \mathrm{When}\mathrm{y}=12, \\ x=17-12 \\ \therefore x=5 \\ \mathrm{Hence},x=12,y=5\mathrm{or}x=5,y=12\text{are}\mathrm{the}\mathrm{solution}\text{s}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$