Question

solve the following system of simultaneous linear equations by the elimination method:
​4 (ii) x - 2y/3 = 8/3
2x/5 - y = 7/5

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{system}\mathrm{of}\mathrm{equations}\mathrm{is}, \\ \mathrm{x}-\frac{2\mathrm{y}}{3}=\frac{8}{3} \\ \Rightarrow 3\mathrm{x}-2\mathrm{y}=8....\left(1\right) \\ \frac{2\mathrm{x}}{5}-\mathrm{y}=\frac{7}{5} \\ \Rightarrow 2\mathrm{x}-5\mathrm{y}=7.....\left(2\right) \\ \mathrm{Multiply}\left(1\right)\mathrm{by}2\mathrm{and}\left(2\right)\mathrm{by}3,\mathrm{we}\mathrm{get} \\ 6\mathrm{x}-4\mathrm{y}=16....\left(3\right) \\ 6\mathrm{x}-15\mathrm{y}=21....\left(4\right) \\ \mathrm{Subtracting}\left(4\right)\mathrm{from}\left(3\right),\mathrm{we}\mathrm{get} \\ -4\mathrm{y}+15\mathrm{y}=16-21 \\ \Rightarrow 11\mathrm{y}=-5 \\ \Rightarrow \mathrm{y}=-\frac{5}{11} \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ 2\mathrm{x}-5\times \left(-\frac{5}{11}\right)=7 \\ \Rightarrow 2\mathrm{x}+\frac{25}{11}=7 \\ \Rightarrow 2\mathrm{x}=7-\frac{25}{11} \\ \Rightarrow 2\mathrm{x}=\frac{52}{11} \\ \Rightarrow \mathrm{x}=\frac{26}{11} \end{gathered}$$