Question

Write the number of solutions of the following pair of linear equations:
$x+3y-4=0,2x+6y-7=0$

Answer 1

The given pair of linear equations are
$$\begin{gathered} x+3y-4=0.....\left(i\right) \\ 2x+6y-7=0.....\left(ii\right) \end{gathered}$$
Which is of the form $a_{1}x+b_{1}y+c_1=0\mathrm{and}{a}_{2}x+b_{2}y+c_2=0$, where $a_1=1,b_1=3,c_1=-4,a_2=2,b_2=6\mathrm{and}{c}_2=-7$
Now
$$\begin{gathered} \frac{a_1}{a_2}=\frac{1}{2} \\ \frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2} \\ \frac{c_1}{c_2}=\frac{-4}{-7}=\frac{4}{7} \\ \Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2} \end{gathered}$$
Thus, the pair of the given linear equations has no solution.