Question

(iii) 4m + 3n = 18; 3m $-$ 2n = 5

Answer 1

$$\begin{gathered} \left(\mathrm{iii}\right)4m+3n=18...\left(1\right) \\ 3m-2n=5...\left(2\right) \\ \mathrm{Multiplying}\mathrm{eq}\left(1\right)\mathrm{by}2\mathrm{and}\mathrm{eq}\left(2\right)\mathrm{by}3,\text{we get}: \\ 8m+6n=36...\left(3\right) \\ 9m-6n=15...\left(4\right) \\ \mathrm{Adding}\left(3\right)\mathrm{and}\left(4\right),\text{we get:} \\ 8m+6n=36 \\ \underline{9m-6n=15} \\ 17m=51 \\ \therefore m=3 \\ \mathrm{Substituting}m=3\mathrm{in}\mathrm{equation}\left(2\right),\text{we get}: \\ 3\times 3-2n=5 \\ \Rightarrow n=\frac{4}{2}=2 \\ \therefore m=3\mathrm{and}n=2\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}s. \end{gathered}$$