No Solutions
(3, 4)
(−4, −3)
Infinitely Many Solutions
What is the relationship between the equations represented by the points (3, 4), (−4, −3), and the concept of infinitely many solutions?
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To determine the types of solutions for a system of equations based on the pairs given:
1. No Solutions: This occurs when the lines are parallel and do not intersect. For example, if you have two equations representing these lines, they will have the same slope but different y-intercepts.
2. Infinitely Many Solutions: This happens when the two equations represent the same line, meaning every point on the line is a solution.
3. Single Solution: This is when the lines intersect at exactly one point.
With the pairs you’ve provided:
– (3, 4) and (−4, −3) could represent points, but without more context (like equations of lines), we can’t plainly categorize them into one of the three categories.
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