Solving Systems and Absolute Value

This video tutorial covers a series of Algebra II problems from the California Standards Test. It begins with solving absolute value equations, demonstrating how to find solutions for equations like |3 - 6x| = 15 and |12 - 4x| = 2. The tutorial then moves on to solving systems of linear equations, including a real-world problem involving the purchase of roses and carnations. It also addresses a system of equations with no solution, explaining the concept of parallel planes. Finally, the video concludes with a problem about calculating the number of bagel packages, reinforcing the application of linear equations in practical scenarios.

What is the complete solution to the equation |3 - 6x| = 15?

• x = 5 or x = -5

• x = 0 or x = 15

• x = 2 or x = -3

• x = -2 or x = 3

What are the possible values of x in the equation |12 - 4x| = 2?

• x = 2.5 or x = 3.5

• x = 1.5 or x = 4.5

• x = 0.5 or x = 5.5

• x = 3 or x = 4

How many dozens of roses did Sherada buy if she bought a total of 17 dozen flowers and spent $192?

• 12 dozens

• 10 dozens

• 8 dozens

• 5 dozens

What is the solution to the system of equations if 2x - y + 3z = 8, x - 6y - z = 0, and -6x + 3y - 9z = 24?

• x = 0, y = 0, z = 0

• x = 1, y = 2, z = 3

• Infinite solutions

• No solution

How many packages of 12 bagels did the manager buy if he bought 20 packages in total and there were 168 bagels?

• 5 packages

• 8 packages

• 10 packages

• 12 packages