Question

the graph of a system of two linear equations is shown. how many solutions does the system have? f. none g. exactly one h. exactly two i. infinitely many

Explanation:

Step1: Analyze the slopes of the lines

The two linear equations are \( y = 2x + 4 \) and \( y = 2x + 2 \). The slope-intercept form of a line is \( y=mx + b \), where \( m \) is the slope. For both equations, the slope \( m = 2 \), so the lines are parallel.

Step2: Determine the number of solutions

Parallel lines (with the same slope and different y - intercepts) never intersect. A solution to a system of linear equations is a point that lies on both lines (the intersection point). Since parallel lines with different y - intercepts never intersect, there are no solutions.

Answer:

F. none