Question

Is the system of linear equations $2x+3y-9=0$ and $4x+6y-18=0$ consistent? Justify your answer.

Answer 1

Given: $2x+3y-9=0$..(i) and $4x+6y-18=0$...(ii)

Here, $a_1=2,b_1=3,c_1=-9$ and $a_2=4,b_2=6,c_1=-18$

Now,

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-9}{-18}=\frac{1}{2}$

Therefore, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, therefore, the system of pair of linear equations are consistent and in-fact are coincident lines.