Solving Systems of Equations and Inequalities

The video tutorial covers solving systems of equations and inequalities. It begins with an introduction to what these systems are, followed by examples and solutions using Desmos. The tutorial explains how to graph systems of equations to find intersection points, which represent solutions. It then transitions to systems of inequalities, explaining how to identify solutions through overlapping shaded areas on graphs. The video provides step-by-step instructions and encourages viewers to practice using Desmos.

What is a system of equations?

• A single equation with multiple variables

• Two or more equations on the same graph

• An equation with no solutions

• A graph with no intersections

What are the solutions to a system of equations?

• Only the y-coordinates that satisfy both equations

• Any points on the graph

• Any x or y coordinates that satisfy both equations

• Only the x-coordinates that satisfy both equations

In Desmos, what indicates the solution to a system of equations?

• The lowest point on the graph

• The points where the two graphs intersect

• The points where the graphs do not intersect

• The highest point on the graph

What is the solution to the system of equations in question 1?

• (0, 1)

• (1, 2)

• (2, 0)

• (2, 1)

How many points of intersection are there in the last system of equations?

• Two

• One

• Three

• Four

What is a system of inequalities?

• Two or more inequalities on the same graph

• A single inequality with multiple variables

• An inequality with no solutions

• A graph with no shaded areas

In a system of inequalities, what represents the solution?

• The lowest point on the graph

• The area with no shading

• The area where the two shades overlap

• The highest point on the graph

What does a dotted line in Desmos indicate for inequalities?

• Equal to

• Greater than or equal to

• Less than or not equal to

• Not equal to

What is the solution to the system of inequalities in question 2?

• The area shaded below the line

• The area shaded above the line

• The area shaded both above and below the line

• The area with no shading

In the last system of inequalities, where is the solution located?

• Inside the circle and above the absolute value

• Outside the circle and below the absolute value

• Inside the circle and below the absolute value

• Outside the circle and above the absolute value