Nonlinear System of Equations

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 do you solve a system of nonlinear equations graphically?

• Set equations equal and solve algebraically

• Add the equations together

• Substitute one equation into another

• Find points of intersection of their graphs

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

If a nonlinear system contains a linear function that never touches the quadratic function, that system has...

• 2 solutions

• 1 solution

• No solutions

• Infinite solutions

If a nonlinear system contains a 2 functions that have NO points of intersection, that system has...

• 2 solutions

• 1 solution

• No solutions

• Infinite solutions

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

• (-4, 2) and (-1, 5)

• (-4, -1) and (2, 5)

• (2, -1 and (-4, 5)

• (-4, 1) and (2, -1)

Find the solution:
y = x² - 4x + 6
y = x + 2

• (3, 1) and (6, 4)

• (-1, 1) and (4, 2)

• (1, 3) and (4, 6)

• (1, 4) and (3, 6)

Solve the system of linear and quadratic equations using substitution:
y = 5
y = 2x² - 16x + 29

• (6, 5) and (2, 5)

• (2, 6)

• (6, 2)

• (5, 6) and (5, 2)

• A
• B
• C
• D