Final answer:
To answer how many solutions a system of equations has, we look at the slopes and y-intercepts of the equations. No solution arises from parallel lines, infinitely many solutions from identical lines, and one solution from intersecting lines with different slopes.
Step-by-step explanation:
To determine which statement describes the system of equations, we can analyze the equations given. If two or more equations have the same slope but different y-intercepts, they are parallel and do not intersect, indicating the system has no solution. If the equations are identical, they represent the same line, and therefore, the system has infinitely many solutions. If two linear equations have different slopes, they will intersect at one point, meaning the system has exactly one solution.
Without the precise system of equations in the question, we can use the general principles to infer the possible scenarios:
- No solution: Parallel lines with equal slopes (m1 = m2) and different y-intercepts (b1 ≠ b2).
- Infinitely many solutions: Identical lines where both the slopes and y-intercepts are the same (m1 = m2 and b1 = b2).
- One solution: Intersecting lines where the slopes are different (m1 ≠ m2).