Question

(vii) $\frac{2x}{3}+\frac{y}{4}=12;\frac{4x}{3}-\frac{9y}{4}=2$

Answer 1

$$\begin{gathered} \frac{2x}{3}+\frac{y}{4}=12 \\ \Rightarrow 8x+3y=144 \\ \Rightarrow x=\frac{144-3y}{8}...\left(\mathrm{i}\right) \\ \frac{4x}{3}-\frac{9y}{4}=2 \\ \Rightarrow 16x-27y=24...\left(\mathrm{ii}\right) \\ \mathrm{Substituting}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{in}\mathrm{eq}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ 16\times \left(\frac{144-3y}{8}\right)-27y=24 \\ \Rightarrow 288-6y-27y=24 \\ \Rightarrow -33y=-264 \\ \therefore y=8 \\ \mathrm{Substitutin}gy=8\mathrm{in}\mathrm{eq}\left(\mathrm{i}\right),\mathrm{we}\mathrm{get}: \\ x=\frac{144-3\times 8}{8} \\ \therefore x=15 \\ \mathrm{Hence},x=15,y=8\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$