Question

comment on type of solution and type of graph of following pair of linear equations :
3x - 5y =11 , 6x-10y = 7

Answer 1

$$\begin{gathered} 3\mathrm{x}-5\mathrm{y}=11...\left(1\right) \\ \mathrm{and} \\ 6\mathrm{x}-10\mathrm{y}=7 \\ 2\left(3\mathrm{x}-5\mathrm{y}\right)=7 \\ 3\mathrm{x}-5\mathrm{y}=\frac{7}{2}....\left(2\right) \\ \mathrm{So}\mathrm{from}\mathrm{equation}1\mathrm{and}2\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that} \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\Rightarrow \frac{3}{3}=\frac{5}{5} \\ \mathrm{So}\mathrm{these}\mathrm{two}\mathrm{lines}\mathrm{are}\mathrm{parallel}. \end{gathered}$$