Question

find the values s of p in the given equations 3x-y-5=0 and 6x-2y-p=0 if the lines respresented by these equation are parallel

Answer 1

$$\begin{gathered} 3\mathrm{x}-\mathrm{y}-5=0 \\ 6\mathrm{x}-2\mathrm{y}-\mathrm{p}=0 \\ \mathrm{Since}\mathrm{lines}\mathrm{are}\mathrm{parallel}\mathrm{that}\mathrm{means}\mathrm{system}\mathrm{of}\mathrm{equations}\mathrm{has}\mathrm{no}\mathrm{solution}. \\ \mathrm{thus}, \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\ne \frac{{\mathrm{c}}_1}{{\mathrm{c}}_2} \\ {\mathrm{a}}_1=3,{\mathrm{a}}_2=6,{\mathrm{b}}_1=-1,{\mathrm{b}}_2=-2,{\mathrm{c}}_1=-5,{\mathrm{c}}_2=-\mathrm{p} \\ \frac{3}{6}=\frac{-1}{-2}\ne \frac{5}{\mathrm{p}} \\ \frac{1}{2}\ne \frac{5}{\mathrm{p}} \\ \mathrm{p}\ne 10. \end{gathered}$$