Determine all values of h and k for which the system s 1 -3x - 3y = h -4x + ky = 10 has no solution. k= ht

The system will have no solution when and .

Step-by-step explanation:

We can find these values by the Gauss-Jordan Elimination method.

The Gauss-Jordan elimination method is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

We have the following system:

This system has the following augmented matrix:

The first thing i am going to do is, to help the row reducing:

Now we have

Now I want to reduce the first row, so I do:

So:

From the second line, we have

The system will have no solution when there is a value dividing 0, so, there are two conditions:

and

...

The system will have no solution when and .