Question

Find the values of k for which the system of equations 3x + ky = 0,
2x – y = 0 has a unique solution.

Answer 1

The given pair of linear equations are
3x + ky = 0                  ……(i)
2x – y = 0                   ……(ii)
Which is of the form ${\displaystyle a_{1}x+b_{1}y+c_1=0\text{and}{a}_{2}x+b_{2}y+c_2=0}$, where
${\displaystyle a_1=3,b_1=k,c_1=0,a_2=2,b_2=-1\text{and}{c}_2=0}$
For the system to have a unique solution, we must have
${\displaystyle \frac{a_1}{a_2}=\frac{b_1}{b_2}}$
${\displaystyle \Rightarrow \frac{3}{2}\ne \frac{k}{-1}}$
${\displaystyle \Rightarrow k\ne –\frac{3}{2}}$
Hence,${\displaystyle k\ne –\frac{3}{2}.}$