Exploring Systems of Equations by Graphing

What are the three methods mentioned for solving a system of equations?

• Graphing, Substitution, Elimination

• Addition, Subtraction, Multiplication

• Division, Reduction, Comparison

• Plotting, Mapping, Tracing

What does a solution of a system represent graphically?

• The slope of a graph

• The x-intercept of a graph

• The y-intercept of a graph

• The point where two graphs intersect

What does it mean if a system of equations is consistent?

• It has at least one solution

• It has exactly one solution

• It has no solution

• It has infinitely many solutions

What does it mean for a system to be consistent and independent?

• It has exactly one solution

• It has no solutions

• It has infinitely many solutions

• It has more than one solution

What is the graphical representation of a consistent and independent system?

• Two parallel lines

• Two perpendicular lines

• Two lines intersecting at a single point

• Two lines overlapping entirely

In the context of graphing systems of equations, what does a horizontal line represent?

• A variable x equal to a constant

• A variable y equal to a constant

• A zero slope

• An undefined slope

How many solutions does a consistent and dependent system have?

• No solutions

• Infinitely many solutions

• Exactly one solution

• Exactly two solutions

What is the result when two equations in a system are identical?

• Infinitely many solutions

• Two solutions

• One solution

• No solution

What characterizes an inconsistent system of equations?

• The system can be solved by substitution

• The system has no solutions

• The system has infinitely many solutions

• The system has one solution

What indicates that two lines are parallel in a graph?

• They have different y-intercepts

• They have the same slope

• They have the same x-intercept

• They intersect at one point