Question

Match the column

$\left(1\right)$ $2x+3y=40$ $6x+5y=10$	$\left(a\right)$ Coincident lines
$\left(2\right)$ $2x+3y=40$ $6x+9y=50$	$\left(b\right)$ Intersecting lines
$\left(3\right)$ $2x+3y=10$ $4x+6y=20$	$\left(c\right)$ Parallel lines

• A. $1\to a,2\to b,3\to c$
• B. $1\to b,2\to a,3\to c$
• C. $1\to b,2\to c,3\to a$
• D. $1\to c,2\to a,3\to b$

Answer 1

The correct option is C $1\to b,2\to c,3\to a$

Write the equations in the form $ax+by+c=0$.

Check for $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ ......(i) for coincident lines,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$ .......(ii) for parallel lines and

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$ .........(iii) intersecting lines.

Then

(1) $2x+3y=40,6x+5y=10$

$\frac{2}{6}\ne \frac{3}{5}$

These line are intersecting lines (b)

(2)$2x+3y=40,6x+9y=50$

$\frac{2}{6}=\frac{3}{9}=\frac{1}{3}\ne \frac{40}{50}=\frac{4}{5}$

These lines are parallel lines (c)

(3)$2x+3y=10,4x+6y=20$

$\frac{2}{4}=\frac{3}{6}=\frac{10}{20}=\frac{1}{2}$

These lines are coincident lines(a)