Question

On comparing the ratios $\frac{a_1}{a_2},\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident:
$2x-y=3;4x-y=5$

• A. Parallel
• B. Coincident
• C. Intersect at a point
• D. None of these

Answer 1

Answer: (C)

Intersect at a point

The equations are
$\Rightarrow 2x-y-3=0$
$\Rightarrow a_1=2,b_1=-1,c_1=-3$
$\Rightarrow 4x-y-5=0$
$\Rightarrow a_2=4,b_2=-1,c_2=-5$
$\text{Comparing}\frac{a_1}{a_2},\frac{b_1}{b_2}\text{and}\frac{c_1}{c_2}$
$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{-1}{-1}=\frac{1}{1}$
$\Rightarrow \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
hence, the given pair of equations has a unique solution therefore the pair of lines intersect at a point.