If the line kx + 4y = 6 passes through the point of intersection of th

1.	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» 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

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»

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