Solving Nonlinear Equations

If |x + 2| = 4, what are the possible values of x?

• 2 and −2

• 6 and −6

• 2 and −6

• 2 and −4

Solve the equation |2x - 5| = 9

• 4 and -4

• 5 and -1

• 6 and -3

• 7 and -2

• Add 3 to both sides

• Subtract 3 from both sides

• Square both sides

• Divide by 2

What is a system of nonlinear equations?

• Involves only linear equations

• Involves at least one non-linear equation

• Always has two solutions

• Cannot be solved graphically

How many solutions can a system of a line and parabola have?

• 0, 1, or 2

• Always 2

• Exactly 1

• Infinite solutions

What happens if the line does not intersect the parabola?

• System has two solutions

• System has one solution

• System has no real solutions

• System has infinite solutions

• 2

• 1

• Infinite

• 0

Create the System of Nonlinear Equations that fits the scenario:

Find two numbers whose sum is 9 and whose product is -36.

• x+y = 9

  xy = -36

• x+y = 9

  x/y = -36

• x-y = 9

  xy = -36

• x-y = 9

  x/y = -36

Create the System of Nonlinear Equations that fits the scenario:

The sum of two numbers is 4 and the difference of their squares is 64.

• x+y = 4
  (x-y)^2 = 64

• x+y = 4
  x^2 - y^2 = 64

• x-y = 4
  (x-y)^2 = 64

• x-y = 4
  x^2-y^2 = 64

Create the System of Nonlinear Equations that fits the scenario: The ratio of two numbers is 5 to 12 and the sum of their squares is 676.

• x/y = 5/12

  x^2+y^2 = 676

• x/y = 5/12

  (x+y)^2 = 676

• x/y = 5/12

  x^2-y^2 = 676

• x/y = 5/12

  (x-y)^2 = 676