Question

Graphically the pair of equations 6x -3y +10 =0 and 2x -y+9 =0 represents two lines which are​

Answer 1

Given:

The pair of equations 6x -3y +10 =0 and 2x -y+9 =0

To find:

The nature of the given lines.

Solution:

1) In the given equations 6x -3y +10 =0 and 2x -y+9 =0, if we compare this with

• a1x+b1y+c1=0

• a2x+b2y+c2=0

we get:

• a1=6, b1= -3, c1= 10

• a2=2, b2= -1, c2=9

2) To find the nature of the equation find the ratio of the coefficients of the equations.

• a1/a2 = 6/2 = 3/1

• b1/b2 = -3/-1 = 3/1

• c1/c2 = 10/9

Hence,

• a1/a2 = b1/b2 ≠ c1/c2

This is the condition of the parallel lines

So. the given lines are parallel to each other.