Question

3x $-$ 2y = 4; 6x + 7y = 19

Answer 1

$$\begin{gathered} \left(vi\right)3x-2y=4...\left(1\right) \\ 6x+7y=19...\left(2\right) \\ \Rightarrow y=\frac{3x-4}{2}...\left(3\right)\left(\mathrm{From}\mathrm{eq}1\right) \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}y\mathrm{in}\mathrm{eq}\left(2\right),\text{we get:} \\ 6x+7\times \left(\frac{3x-4}{2}\right)=19 \\ \Rightarrow \frac{12x+21x-28}{2}=19 \\ \Rightarrow 33x-28=38 \\ \Rightarrow 33x=66 \\ \Rightarrow x=2 \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\mathrm{eq}\left(3\right),\text{we get:} \\ y=\frac{3\times 2-4}{2} \\ \Rightarrow y=1 \\ \therefore x=2,y=1\mathrm{is}\mathrm{the}\mathrm{solution}. \end{gathered}$$