Question

What will be the value of k, if the lines given by x+ky+3 and 2x+(k+2)y+6 are coincident?

(a) 4

(b) 2

(c) 6

(d) 8

The question was asked during an interview for a job.

My doubt is from Solution of Two Linear Equations in Two Variables in Different Methods in chapter Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

The correct option is (b) 2

To explain: The given equations are x+ky+3 and (k-1)x+4y+6.

Here, a1=1, b1=k, c1=3 and a2=k-1, b2=4, c2=6

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

Now, \(\frac {a_1}{a_2} = \frac {1}{k-1}, \frac {b_1}{b_2} =\frac {k}{4}, \frac {c_1}{c_2} =\frac {3}{6}\)

\(\frac {1}{k-1}=\frac {k}{4}=\frac {1}{2}\)

2k=4

k=2