Question

Given the four lines with the equations

x + 2y - 3 = 0, 3x + 4y -7 = 0,

2x + 3y - 4 = 0, 4x + 5y - 6 = 0

then

(a) they are all concurrent

(b) they are the sides of a quadrilateral

(c) only three lines are concurrent

(d) None of the above

Answer 1

Correct option: (c) only three lines are concurrent

Explanation:

Given lines, x + 2y- 3 = 0 and 3x + 4y - 7= 0 intersect at (1,1), which does not satisfy 2x + 3y - 4 = 0 and 4x + 5y - 6 = 0. Also, 3x + 4y- 7 = 0 and 2x + 3y - 4 = 0 intersect at (5, -2) which does not satisfy x + 2y - 3 = 0 and 4x + 5y - 6= 0. 

Lastly, intersection point of x + 2y - 3 = 0 and 2x + 3y - 4 = 0 is (-1, 2) which satisfy 4x + 5y - 6 = 0. Hence, only three lines are concurrent.