Question

choose the statement that correctly describes how many solutions there are for this system of equations. click the icon to view a graph for the system of equations. choose the correct answer below. a. no solution because the slopes are equal and the y-intercepts are not equal b. exactly one solution because the slopes are equal but the y-intercepts are not equal c. exactly one solution because the slopes are not equal d. infinitely many solutions because the slopes are equal and the y-intercepts are equal

Explanation:

To determine the number of solutions for a system of linear equations (in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept):

• If the slopes (\(m\)) are not equal, the lines intersect at exactly one point, so there is exactly one solution (Option C).
• If the slopes are equal and the y - intercepts (\(b\)) are not equal, the lines are parallel and never intersect, so there is no solution (Option A).
• If the slopes are equal and the y - intercepts are equal, the lines are coincident (the same line), so there are infinitely many solutions (Option D).
• Option B is incorrect because if slopes are equal and y - intercepts are not equal, there is no solution, not one solution.

Answer:

C. Exactly one solution because the slopes are NOT equal