Question
Question 2:
Infinite Solutions
When you solve equations with infinite solutions... do you get (choose one below)
0x = 0
correct scenario)
Ox = any #
x= any # (circle the
What does it mean on a graph to have infinite solutions? Explain what you would see.
Infinite Solutions
When you solve equations with infinite solutions... do you get (choose one below)
0x = 0
correct scenario)
Ox = any #
x= any # (circle the
What does it mean on a graph to have infinite solutions? Explain what you would see.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
When you solve equations and find that there are infinite solutions, you typically end up with a scenario represented by the equation \(0x = 0\). This occurs when you have two equations that are essentially the same or when one equation can be derived from the other.
### What Does It Mean on a Graph?
In terms of graphing, having infinite solutions means that the two equations represent the same line in a coordinate system. This means:
- The lines are coincident, meaning they overlap completely.
- Every point on the line corresponds to a solution of the system of equations.
### What You Would See
On a graph, you would see one straight line rather than two distinct lines. For example, if you graphed the equations \(y = 2x + 3\) and \(2y = 4x + 6\), both equations are equivalent and represent the same line.
Because every point on the line is a solution, this is visually represented as a single line where the set of all points (x, y) that lies on that line is the solution to the system. There are no intersections or separate lines; they completely overlap at every point.
### What Does It Mean on a Graph?
In terms of graphing, having infinite solutions means that the two equations represent the same line in a coordinate system. This means:
- The lines are coincident, meaning they overlap completely.
- Every point on the line corresponds to a solution of the system of equations.
### What You Would See
On a graph, you would see one straight line rather than two distinct lines. For example, if you graphed the equations \(y = 2x + 3\) and \(2y = 4x + 6\), both equations are equivalent and represent the same line.
Because every point on the line is a solution, this is visually represented as a single line where the set of all points (x, y) that lies on that line is the solution to the system. There are no intersections or separate lines; they completely overlap at every point.
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