Solving Systems of Equations by Graphing

The video tutorial introduces eighth-grade students to solving systems of equations, focusing on the graphing method. It covers key vocabulary such as consistent, independent, dependent, and inconsistent systems. Through examples, students learn how to graph equations to find solutions, including a real-world problem involving alligator growth. The tutorial explains different types of solutions: one solution, infinitely many solutions, and no solution, highlighting their characteristics. The video concludes with final examples and a summary of key concepts.

What is the first method introduced for solving systems of equations?

• Substitution

• Elimination

• Matrix Method

• Graphing

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

• (1, 2)

• (2, 4)

• (4, 6)

• (3, 5)

How do you verify the solution of a system of equations?

• By substituting the solution back into the original equations

• By calculating the area between the lines

• By checking if the lines are parallel

• By finding the midpoint of the lines

In the alligator growth example, what is the initial weight of Alligator 1?

• 2 pounds

• 4 pounds

• 6 pounds

• 8 pounds

After how many months do the two alligators weigh the same?

• 5 months

• 4 months

• 3 months

• 2 months

What type of solution is it when two lines intersect at one point?

• Dependent solution

• Infinitely many solutions

• One solution

• No solution

What is the characteristic of a consistent dependent system?

• Different slopes and different y-intercepts

• Same slope and same y-intercept

• Same slope and different y-intercepts

• Different slopes and same y-intercept

What does it mean if two lines are parallel on a graph?

• They intersect at one point

• They have the same slope and same y-intercept

• They have the same slope and different y-intercepts

• They have different slopes and different y-intercepts

What type of solution does a system have if the lines are parallel?

• Dependent solution

• One solution

• Infinitely many solutions

• No solution

If two equations have the same slope and y-intercept, what type of solution do they have?

• Infinitely many solutions

• Inconsistent solution

• No solution

• One solution