Question

In the system of equations below, k is a constant. If the system has infinitely many solutions, what is the value of k?

Options:
A) k = -10
B) k = -20
C) k = 0
D) k = 10

Answer 1

The value of k that would result in infinitely many solutions is k = 2.

Step-by-step explanation:

A system of linear equations has infinitely many solutions when the equations are dependent, meaning that one equation can be obtained by multiplying the other equation(s) by a constant factor. In this case, the value of k that would result in infinitely many solutions can be determined by setting the coefficients of the variables in the two equations equal to each other:

2k = 4

From this equation, we can solve for k:

k = 2

Therefore, the value of k that would result in infinitely many solutions is k = 2. None of the options provided match this value, so the correct answer is none of the above.