Answer:
Step-by-step explanation:
3x1+ x2= 2 , kx1 + 2x2= 4
are the two equations in the system
We have to find k values for which the system of linear equations have zero, one, or an infinite number of solutions
The determinant value would be
[tex]\left[\begin{array}{ccc}3&1\\k&2\end{array}\right] \\=6-k[/tex]
This determinant is 0 if k =6
Otherwise the system has a unique solution
One solution if k ≠6
Case 2: If k =6
3x1+x2 = 2
6x2+2x2 = 4
We find that when I equation is multiplied by 2, we get the second equation.
i.e. all the points in this line satisfy this system.
Infinite solutions are there when k =6
