Question

Ben says this system of equations has one solution. Is he correct? Explain. Choose the correct answer below.Y= 1/4x-4Y= 1/4x-14 A. Ben is incorrect. Since the equations have the same slope, the system has infinitely many solutions. B. Ben is incorrect. Since the equations have the same slope and different y-intercepts, the system has no solution. C. Ben is correct. Since the equations have the same slope, the system has exactly one solution.D. Ben is correct. Since the equations have the same slope and different y-intercepts, the system has exactly one solution.

Answer 1

Let's begin by listing out the given information:

$\begin{gathered} y=\frac{1}{4}x-4--------1 \\ y=\frac{1}{4}x-14-------2 \\ \end{gathered}$

We will observe that both equations have the same slope but different y-intercept. This implies that both equations are parallel to one another. This means that both equations never intersect at any point & as such, have no solution.

Hence, the correct answer is B. Ben is incorrect. Since the equations have the same slope and different​ y-intercepts, the system has no solution.