Question

In the system of equations above, k is a constant. If the system of equations has no solution, what is the value of 2k?

a) k
b) 2k
c) 0
d) -2k

Answer 1

The value of 2k when the system of equations has no solution is 0.

Step-by-step explanation:

If the system of equations has no solution, it means that the lines represented by the equations are parallel and will never intersect. In this case, the determinant of the coefficient matrix is 0. The determinant can be found by subtracting the product of the top left and bottom right elements from the product of the top right and bottom left elements. So, if the determinant is 0, we can conclude that there is no solution.

For the given options, we can see that only option (c) 0 is correct. Therefore, the value of 2k when the system of equations has no solution is 0.