Question

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: Not all three possibilities need occur.] 3x1+ x2= 2 , kx1 + 2x2= 4

Answer 1

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

`\left[\begin{array}{ccc}3&1\\k&2\end{array}\right] \\=6-k`

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