Which out of the following type of straight lines will be represented by the system of equations $3

Question

Which out of the following type of straight lines will be represented by the system of equations $3 x+4 y=5$ and $6 x+8 y=7$ ?\

Professor PC Thomas Classes · Answer

(a): Given equations are $3 x+4 y=5$\ $\Rightarrow 3 x+4 y-5=0$\ and $6 x+8 y=7 \Rightarrow 6 x+8 y-7=0$\ Here, $a_{1}=3, b_{1}=4, c_{1}=-5$\ and $a_{2}=6, b_{2}=8, c_{2}=-7$\ Now, $\frac{a_{1}}{a_{2}}=\frac{3}{6}=\frac{1}{2} ; \frac{b_{1}}{b_{2}}=\frac{4}{8}=\frac{1}{2}$\ and $\frac{c_{1}}{c_{2}}=\frac{-5}{-7}=\frac{5}{7}$\ $	herefore \quad \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} 
eq \frac{c_{1}}{c_{2}}$\ ∴ The given pair of straight lines are parallel.