Question

Select the correct option from the given alternatives:

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 =

Options

• 1

• 2

• 3

• 4

Answer 1

2

Explanation:

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