Solving Quadratic Equations and Systems

The video tutorial explains how to solve a system of equations where the sum of the squares of two numbers is 320 and their difference is eight. The method of substitution is used to solve the equations, leading to a quadratic equation that is expanded, simplified, and factored to find the solutions. The solutions are verified both algebraically and graphically, demonstrating two sets of solutions: one positive and one negative.

What is the sum of the squares of the two numbers?

• 320

• 8

• 64

• 256

What is the difference between the two numbers?

• 8

• 320

• 16

• 0

Which equation represents the sum of the squares of the numbers?

• x^2 - y^2 = 8

• x + y = 320

• x - y = 8

• x^2 + y^2 = 320

What method is used to solve the system of equations?

• Matrix

• Substitution

• Graphing

• Elimination

What is the first step in solving the quadratic equation by factoring?

• Identifying the greatest common factor

• Graphing the equation

• Finding the roots

• Completing the square

What are the factors of the quadratic equation after factoring?

• y and 8

• y^2 and 16

• y + 8 and y - 16

• y - 8 and y + 16

What are the possible values for y after solving the quadratic equation?

• 8 and -16

• 0 and 8

• 8 and 16

• 16 and -8

What is the corresponding value of x when y is 8?

• 16

• 8

• 0

• -8

What is the ordered pair solution when y is -16?

• (-16, -8)

• (8, 16)

• (-8, -16)

• (16, 8)

How can the solutions be verified graphically?

• By solving algebraically

• By plotting the equations and checking intersections

• By estimating

• By using a calculator