Solving Linear Quadratic Systems through Graphing

The video tutorial covers solving linear quadratic systems by graphing. It explains how systems of equations can have one, two, or no real solutions based on graph intersections. The tutorial includes examples demonstrating each scenario: one solution, two solutions, and no solutions. It also provides guidance on using graphing calculators and verifying solutions.

What is a system of equations?

• A graph with no intersections

• An equation with no variables

• Two or more equations used simultaneously

• A single equation with multiple variables

What do the points where the graphs of a system intersect represent?

• The solutions to the system

• The minimum values of the equations

• The maximum values of the equations

• The points where the equations are undefined

How many real solutions can a linear quadratic system have?

• Only two

• Zero, one, or two

• One, two, or three

• Only one

In the first example, what is the solution to the system?

• (0, -2)

• (-2, 0)

• (2, 0)

• (0, 2)

How can you verify the solution to a system of equations?

• By solving the equations algebraically

• By using a different graphing calculator

• By checking if the point satisfies both equations

• By graphing the equations again

In the second example, how many intersection points are there?

• Two

• One

• None

• Three

What are the solutions in the second example?

• (-1, 3) and (2, -6)

• (1, 3) and (2, -6)

• (1, -3) and (-2, 6)

• (1, 3) and (-2, -6)

What is the result when the graphs do not intersect at all?

• One real solution

• Infinite solutions

• Two real solutions

• No real solutions

In the final example, what type of graph is used in place of the quadratic function?

• A straight line

• A circle

• A hyperbola

• An ellipse

What is the solution in the final example?

• (-3, 4)

• (4, -3)

• (-4, 3)

• (3, -4)