Question

1. if a system of linear equations has one solution, what does this mean about the two lines?
2. if a system of linear equations has no solution, what does this mean about the two lines?
3. if a system of linear equations has infinitely many solutions, what does this mean about the two lines?

Explanation:

1. A single solution occurs where two lines intersect at exactly one unique point, meaning they have different slopes.
2. No solution means the lines never meet; they are parallel and distinct, so they have identical slopes but different y-intercepts.
3. Infinitely many solutions mean the two lines are exactly the same (coinciding), so every point on one line is on the other, with identical slopes and y-intercepts.

Answer:

1. The two lines intersect at exactly one unique point (they are non-parallel and distinct).
2. The two lines are parallel and distinct, so they never intersect.
3. The two lines are coinciding (identical), so every point on one line is a solution.