Solving Systems of Equations by Graphing

What defines a system of equations?

• A mathematical expression without variables

• Two or more equations graphed on the same coordinate plane

• A single equation with multiple variables

• A set of equations plotted on different coordinate planes

What does it mean if a system of equations has multiple solutions?

• The graphs intersect at more than one point

• The graphs do not intersect at all

• The equations are not dependent on each other

• The graphs intersect at exactly one point

What is the ordered pair for the first solution in the multiple solutions example?

• (-1, 6)

• (1, -6)

• (4, -3)

• (-4, 3)

What does the intersection point of (-4, 3) signify in the context of systems of equations?

• One of the multiple solutions to the system

• A point where lines are parallel

• The only solution to the system

• A point where three lines intersect

In the single solution example, what is the ordered pair where the graphs intersect?

• (-4, 1)

• (-1, 2)

• (4, -1)

• (1, -2)

What type of solution is present when two graphs intersect at exactly one point?

• Infinite solutions

• Two solutions

• No solution

• One solution

How many solutions does a system have if the graphs do not intersect?

• No solution

• One solution

• Two solutions

• Multiple solutions

Which scenario describes a system with no solution?

• All graphs are parallel

• Graphs do not intersect

• Graphs intersect at multiple points

• Graphs intersect at one point

What is the ordered pair for the intersection in the last example discussed?

• (1, -2)

• (-4, 1)

• (4, -1)

• (-1, 2)

If a system of equations' graphs cross at the point (-1, 2), what does this indicate?

• The system's equations are inconsistent

• The system has multiple solutions

• The system has exactly one solution

• The system has no solution