Question

10. Solve the following pair of equations for x and y, also find the value of ‘m’ such that 𝑦=𝑚𝑥+2.
𝑥+3/𝑦=5 , 2𝑥−6/𝑦=6.​

Answer 1

$$\begin{gathered} 1.x+\frac{3}{y}=5\equiv \mathbf{2}\mathit{x}\mathbf{}\mathbf{+}\frac{\mathbf{6}}{\mathbf{y}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{10} \\ 2.2x-\frac{6}{y}=6 \\ Adding1.and2. \\ \Rightarrow 2x+\frac{6}{\mathrm{y}}+2x-\frac{6}{y}=10+6 \\ \Rightarrow 4x=16 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4} \\ putthisbackin1. \\ \Rightarrow 2x\left(4\right)+\frac{6}{\mathrm{y}}=10 \\ \Rightarrow \frac{6}{y}=2\Rightarrow \mathbf{}\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3} \\ \mathit{G}\mathit{i}\mathit{v}\mathit{e}\mathit{n}\mathbf{}\mathit{t}\mathit{h}\mathit{a}\mathit{t}\mathbf{,}\mathbf{}\mathit{y}\mathbf{=}\mathbf{}\mathit{m}\mathit{x}\mathbf{+}\mathbf{2} \\ \mathit{p}\mathit{l}\mathit{u}\mathit{g}\mathit{g}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{t}\mathit{h}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{s}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathbf{}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3} \\ \mathbf{\Rightarrow }\mathbf{3}\mathbf{}\mathbf{=}\mathbf{}\mathit{m}\mathbf{4}\mathbf{+}\mathbf{2} \\ \mathbf{\Rightarrow }\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{4}} \end{gathered}$$