FINAL EXAM 24-25

The graphs of three systems of equations are shown below. Which system has only one solution?

• System I

• System II

• Systems II & III

• None of these

Jeremy writes the following system of equations: y = x² + 10x + 29 y = 2x + 13 How many solutions will this system have?

• 2

• 0

• 1

• 3

• E. x = 10

• C. x = 6

• D. x = 8

• A. x = 2

• B. x = 5

• (2, 10), (3, 33)

• (2, 12), (4, 18)

• (2, 22), (18, 4)

• (2, -10), (1, 7)

• m = -1

• m = 5

• m = -0.5

• m = 0

• b = -6

• b = 7

• b = 9

• b = 2

• x = 1,000

• x = 500

• x = 250

• x = 125

While solving the square root equation 2x – 6 = 4√(3 – x), Luca writes the associated quadratic equation 48 – 16x = 4x² – 24x + 36. He solves this quadratic equation, obtaining x = –1 and x = 3. Which of Luca’s solutions is an extraneous solution of the original square root equation and why?

• 3 is an extraneous solution of the square root equation because it makes both sides of the square root equation equal to 0.

• –1 is an extraneous solution of the square root equation because it makes both sides of the quadratic equation equal to 1.

• 3 is an extraneous solution of the square root equation because it satisfies both the quadratic equation and the square root equation.

• –1 is an extraneous solution of the square root equation because it satisfies the quadratic equation but not the square root equation.

• –2

• 3

• 6

• 10

• –2

• 3

• 6

• 10