DeeptiM wrote:

A given line L has an equation 3x+4y=5. Which of the following is the equation of line

which doesnot intersect the above line?

1) 4x+3y=5

2) 3x+4y=10

3) 3x+5y=5

4) 3x+5y=3

5) 3x-4y=5

Can anyone pls help me understand a simplest way to solve such questions..

I will share the answer after few explanations..

The only way 2 lines lying on the xy axis will not intersect is if they are distinct parallel lines.

Say, the equation of 2 lines is:

ax + by + c = 0

mx + ny + p = 0

These two lines intersect in a single point if:

\(\frac{a}{m} \neq \frac{b}{n}\)

These two lines are distinct and parallel if:

\(\frac{a}{m} = \frac{b}{n} \neq \frac{c}{p}\)

They are the same line if:

\(\frac{a}{m} = \frac{b}{n} = \frac{c}{p}\)

Since you want to find parallel distinct lines i.e. no point of intersection, \(\frac{a}{m} = \frac{b}{n} \neq \frac{c}{p}\) should hold.

given: 3x+4y=5

parallel: 3x+4y=10

What if the question is to find a point at which the line intersect 3x+4y=5?