The value of k for which the lines 3x + 4y = 5, 5x + 4y = 4 and kx + 4y = 6 meet at a point is

a. 1 b. 2 c. 3 d. 4

Question

The value of k for which the lines 3x + 4y = 5, 5x + 4y = 4 and
kx + 4y = 6 meet at a point is
a 1 b 2 c 3 d 4

Chetna Khanna · Accepted Answer

Given equations are :

3x + 4y = 5, 5x + 4y = 4 and kx + 4y = 6

Solving equations, 3x + 4y = 5 and 5x + 4y = 4 for x and y.

$15 x + 20 y = 25 15 x + 12 y = 12 \underset{̲}{- - -} 8 y = 13 \Rightarrow y = \frac{13}{8} 3 x + 4 y = 5 \Rightarrow 3 x + 4 \times \frac{13}{8} = 5 \Rightarrow 3 x + \frac{13}{2} = 5 \Rightarrow 3 x = 5 - \frac{13}{2} \Rightarrow 3 x = \frac{10 - 13}{2} \Rightarrow 3 x = \frac{- 3}{2} \Rightarrow x = \frac{- 3}{2} \times \frac{1}{3} \Rightarrow x = \frac{- 1}{2}$

Putting the values of x and y in the equation kx + 4y = 6.

$k (\frac{- 1}{2}) + 4 (\frac{13}{8}) = 6 \Rightarrow \frac{- k}{2} + \frac{13}{2} = 6 \Rightarrow \frac{- k}{2} = 6 - \frac{13}{2} \Rightarrow \frac{- k}{2} = \frac{12 - 13}{2} \Rightarrow \frac{- k}{2} = \frac{- 1}{2} \Rightarrow k = 1$

Thus, the correct answer is a.

The value of k for which the lines 3x + 4y = 5, 5x + 4y = 4 and kx + 4y = 6 meet at a point is a. 1 b. 2 c. 3 d. 4

The value of k for which the lines 3x + 4y = 5, 5x + 4y = 4 and kx + 4y = 6 meet at a point is

a. 1 b. 2 c. 3 d. 4