Question

What will be the value of k, if the lines given by (5+k)x-3y+15 and (k-1)x-y+19 are parallel?

(a) 5

(b) 4

(c) 6

(d) 7

I had been asked this question during an interview.

The query is from Solution of Two Linear Equations in Two Variables in Different Methods in portion Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

Correct option is (b) 4

For explanation: The given equations are (5+k)x-3y+15 and (k-1)x-y+19.

Here, a1=5+k, b1=-3, c1=15 and a2=k-1, b2=-1, c2=19

Lines are parallel, so \(\frac {a_1}{a_2} = \frac {b_1}{b_2} \ne \frac {c_1}{c_2} \)

Now, \(\frac {a_1}{a_2} = \frac {5+k}{k-1}, \frac {b_1}{b_2} =\frac {-3}{-1}\) = 3, \(\frac {c_1}{c_2} = \frac {15}{19} \)

\(\frac {5+k}{k-1}\) = 3

5+k=3(k-1)

5+k=3k-3

5+3=3k-k

2k=8

k=4