Q1. Determine the value of k for which the given system of equations has unique solution:

Question

a) 2x – 3y = 1 ; k x + 5y = 7 b) 4x – 5y = k ; 2x – 3 y = 12

Answer 1

a)

2x-3y = 1
kx+5y = 7

There is no single value of k which determines a unique solution. In fact, since the slope of

2x-3y=1 is 2/3, any value of k which makes the slope of the other line different from 2/3 will work.

So, if -k/5 = 2/3 then k = -10/3 and the line

-10/3 x + 5y = 7

is parallel to the first line.

So, any k different from -10/3 will produce a single solution.

The other pair of lines is even easier. Since it is clear that the lines have different slopes, they must intersect at a single point, regardless of k's value.