Question

(v) 5x + 2y = 13; 4x − 3y = 15

Answer 1

$$\begin{gathered} 5x+2y=13 \\ \Rightarrow x=\frac{13-2y}{5}...\left(\mathrm{i}\right) \\ 4x-3y=15....\left(\mathrm{ii}\right) \\ \mathrm{Substituting}\text{eq}\left(\mathrm{i}\right)\mathrm{in}\text{eq}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ 4\times \left(\frac{13-2y}{5}\right)-3y=15 \\ \Rightarrow 52-8y-15y=75 \\ \Rightarrow -23y=23 \\ \Rightarrow y=-1 \\ \mathrm{Substituting}y=-1\mathrm{in}\mathrm{eq}\left(\mathrm{i}\right),\mathrm{we}\mathrm{get}: \\ x=\frac{13-2\times \left(-1\right)}{5} \\ \Rightarrow x=3 \\ \mathrm{Hence},x=3,y=-1\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$