Does the system of equations y=1/2x−3

Question

and y=1/2x+2
describe a zero solution system or an infinite solution system? Enter 1 for zero or 2 for infinite.(1 point)

Answer 1

The given system of equations is:

1. \( y = \frac{1}{2}x - 3 \)
2. \( y = \frac{1}{2}x + 2 \)

To determine the type of solution system, we can compare the two equations.

Both equations have the same slope (\( \frac{1}{2} \)), which means they are parallel lines. However, they have different y-intercepts (\(-3\) and \(+2\)), which indicates that they will never intersect.

Since the lines are parallel and do not overlap at any point, this system of equations has zero solutions.

So, the answer is \(1\) for a zero solution system.