Question

(vii) 4x + y = 34, x + 4y = 16

Answer 1

$$\begin{gathered} 4x+y=34...\left(\mathrm{i}\right) \\ x+4y=16...\left(\mathrm{ii}\right) \\ \mathrm{Multiplying}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{by}4,\mathrm{we}\mathrm{get}: \\ 4x+16y=64...\left(\mathrm{iii}\right) \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{from}\left(\mathrm{iii}\right),\text{we get}: \\ 4x+16y=64 \\ 4x+y=34 \\ \underline{---} \\ 15y=30 \\ \therefore y=2 \\ \mathrm{Substituting}y=2\mathrm{in}\left(\mathrm{i}\right),\mathrm{we}\mathrm{get}: \\ 4x+2=34 \\ \Rightarrow 4x=32 \\ \therefore x=8 \\ \mathrm{Hence},x=8,y=2\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$