Question

If the line kx + 4y = 6 passes through the point of intersection of the two lines 2x + 3y = 4 and 3x + 4y = 5, then k =

(a) 1 

(b) 2 

(c) 3 

(d) 4

Answer 1

Correct option is : (b) 2

Given two lines are 

2x + 3y = 4 ……(i) 

3x + 4y = 5 …….(ii) 

Multiplying (i) by 3 and (ii) by 2 and then subtracting, we get y = 2 

Substituting y = 2 in (i), we get x = -1 

∴ Point of intersection of lines (i) and (ii) is (-1, 2). 

Given that the line kx + 4y = 6 passes through (-1, 2). 

k(-1) + 4(2) = 6 

∴ k = 2