Questions: y=1/2 x-1 y=1/2 x+5 How many solutions does the system of equations have? no solution one solution infinitely many solutions

Solution Steps

The given system of equations is: \[ y = \frac{1}{2}x - 1 \quad \text{and} \quad y = \frac{1}{2}x + 5 \]

Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. For the first equation, the slope \( m = \frac{1}{2} \), and for the second equation, the slope \( m = \frac{1}{2} \). Since the slopes are equal, the lines are parallel.

The y-intercept for the first equation is \( b = -1 \), and for the second equation, it is \( b = 5 \). Since the y-intercepts are different, the lines do not intersect.

Since the lines are parallel and do not intersect, the system of equations has no solution.

Final Answer