Question

For what value of k, the system of equations
$x+2y=5$
$3x+ky-15=0$
has a unique solution?

Answer 1

The given system of equations can be written as
$x+2y-5=0$
$3x+ky-15=0$

This system of equation is of the form
$a_{1}x+b_{1}y+c_1=0$
$a_{2}x+b_{2}y+c_2=0$

where, $a_1=1,b_1=2,c_1=-5$ and $a_2=3,b_2=k,c_2=-15$

The given system of equations will have a unique solution, if

$\frac{1}{3}\ne \frac{2}{k}\Rightarrow k\ne 6$.