Question

What is the nature of the three lines represented by x+3y=6,5x-2y=13,2x-3y=3?

Answer 1

Answer:

here determinant is not equal to 0 hence non intersecting lines

Answer 2

Given:

x + 3y = 6

5x - 2y = 13

2x - 3y = 3

To find:

What is the nature of the three lines represented by x + 3y = 6, 5x - 2y = 13, 2x - 3y = 3?

Solution:

Consider the attached figure, while going through the following steps.

The given lines meet or intersect at a point (3, 1), as this point satisfies all the above three equations.

It implies that, these lines are not parallel and have a unique solution.

Verification:

x + 3y = 6

(3) + 3 (1) = 6

3 + 3 = 6

6 = 6

5x - 2y = 13

5 (3) - 2 (1) = 13

15 - 2 = 13

13 = 13

2x - 3y = 3

2 (3) - 3 (1) = 3

6 - 3 = 3

3 = 3