Solving a System of Equations

The video tutorial explains how to find two positive numbers given their difference and the sum of their squares. It sets up a system of equations, solves it using substitution, simplifies the resulting quadratic equation, and finds the solution by factoring. The final solution identifies the two numbers as 2 and 9.

What is the difference between the two positive numbers?

• 7

• 5

• 6

• 8

How is the sum of the squares of the two numbers expressed?

• x + y = 85

• x^2 + y = 85

• x^2 + y^2 = 85

• x^2 - y^2 = 85

What method is used to solve the system of equations?

• Substitution

• Matrix

• Elimination

• Graphing

What is the expression for x after solving the first equation?

• x = y + 7

• x = 7 - y

• x = 7 + y

• x = y - 7

What is the result of squaring the binomial (7 + y)?

• 49 + 7y

• 14y + y^2

• 49 + y^2

• 49 + 14y + y^2

What is the quadratic equation obtained after substitution?

• y^2 + 7y - 36 = 0

• 2y^2 + 7y - 36 = 0

• y^2 + 14y - 36 = 0

• 2y^2 + 14y - 36 = 0

What is the greatest common factor factored out from the quadratic equation?

• 4

• 3

• 1

• 2

What are the factors of the trinomial y^2 + 7y - 18?

• (y + 9)(y - 2)

• (y + 6)(y - 3)

• (y + 2)(y - 9)

• (y + 3)(y - 6)

What is the value of y after solving the factored equation?

• 9

• 2

• -2

• -9

What are the two positive numbers found?

• 7 and 2

• 9 and 7

• 9 and 2

• 2 and 9