Question

The lines represented by 4x+5y=3 and 16x + 20y = 6 are (a) intersecting (b) coincident (c) parallel(d) none of these​

Answer 1

Given: The lines represented by 4x+5y=3 and 16x+20y= 6 is given

To find: If the lines are intersecting,parallel or coincident

Explanation: For given two equations, the lines are intersecting when there is one solution to the equation, parallel when there are no solution and coincident when there are infinitely many solutions.

Let:

a1= coefficient of x in 4x+5y=3

=4

b1= coefficient of y in 4x+5y=3

=5

c1= constant term=3

a2= coefficient of x in 16x+20y=6

=16

b2= coefficient of y in 16x+20y=6

=20

c2= constant term=6

Taking ratio of the coefficients we get:

a1/a2= 4/16

=1/4

b1/b2= 5/20

= 1/4

c1/c2= 3/6

= 1/2

Here,

a1/a2 = b1/b2 = 1/4 which is not equal to c1/c2= 1/2

This is the condition when there is not a single solution to the question. Therefore, the lines are parallel because of the explanation given above.

The lines represented by lines 4x+5y=3 and 16x+15y= 6 represent parallel lines.