QuestionWhat is the difference between the graph of an equation in the system and the graph of the system's solution set? A. The graph of an equation is a point whereas the graph of the system's solution set is an infinite number of points. B. The graph of an equation is a line whereas the graph of the system's solution set is a point. C. The graph of an equation is a line whereas the graph of the system's solution set is a blank graph. D. There is no difference.
Studdy Solution
STEP 1
1. A system of equations consists of two or more equations.
2. The graph of an equation refers to the visual representation of all solutions to that single equation.
3. The graph of a system's solution set refers to the visual representation of all solutions that satisfy all equations in the system simultaneously.
STEP 2
1. Understand the graph of a single equation.
2. Understand the graph of the solution set of a system of equations.
3. Compare and contrast the two graphs.
STEP 3
The graph of a single equation in a system is typically a line (or curve) representing all solutions to that equation.
For example, in a system of linear equations, each equation is represented by a line on a graph.
STEP 4
The graph of the system's solution set is the intersection of the graphs of all equations in the system.
In a system of linear equations, this intersection is typically a point where the lines intersect, representing the solution that satisfies all equations.
STEP 5
Compare the graph of an individual equation (a line) to the graph of the system's solution set (a point of intersection).
The graph of an equation is a line, whereas the graph of the system's solution set is a point.
The correct answer is:
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