Question

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

3x - 7y = k
-6x + 14y = 20
a) k = 10
b) k = -10
c) k = 20
d) k = -20

Answer 1

The value of k that would result in the system of equations having infinitely many solutions is k = -30.

Step-by-step explanation:

To determine the value of k in the system of equations, we can use the method of elimination. By multiplying the first equation by 2 and the second equation by -3, we can eliminate the x term:

6x - 14y = 2k

6x - 14y = -60

Now, we can subtract the second equation from the first equation:

0 = 2k + 60

By simplifying the equation, we get:

2k = -60

k = -30

Therefore, the value of k that would result in the system of equations having infinitely many solutions is k = -30.