How to solve the following system of equation?

Question

Given two equations:

$2mx+6y =1$ and

$4x -(1-m)y = -16$

Find the value of $m$, such that the system has no solution?

My attempt:

From the first:

$2mx = 1-6y$

Then $x= (1-6y)/(2m)$

Substitute to the second equation to get:

$2(1-6y)/m -(1-m)y =-16$

Simplify to get

$2(1-6y)- m(1-m)y+16m = 0$

Until there, I got stuck. How can we deal with the two variables?

I think I need to use the discriminant to solve this, but from where must I started?

Thanks

Answer 1

Hint :

Let

$A=\begin{vmatrix} 2m & 6 \\ 4 & -(1-m) \end{vmatrix}$

Then , the system has no solution if : $\det(A)=0$