1 of 7 Pre-Calculus2 Chapter 10 Section 8 Warm up Write the equation in standard form of Write the equation in standard form of Then find the coordinates of the focus, and vertex. Then find the coordinates of the focus, and vertex. Write the equations of the directrix and axis of symmetry Write the equations of the directrix and axis of symmetry

Solving Systems of Second Degree Equations and Inequalities Chapter 10 Section 8 Objective: To graph and solve systems of second degree equations and inequalities

3 of 7 Pre-Calculus2 Chapter 10 Section 8 Linear - Quadratic Equations

4 of 7 Pre-Calculus2 Chapter 10 Section 8 Solve the system of equations Use substitution. First rewrite 4y – x = 3 as x = 4y – 3 x 2 – 4y 2 = 9 (4y – 3) 2 – 4y 2 = 9 (4y – 3) 2 = 16y 2 – 24y y 2 – 24y = 0 → y 2 – 2y = 0 → y(y – 2) = 0 y = 0 and y = 2. x = 4(0) – 3 x = 4(2) – 3 x = –3 x = 5 (–3, 0) (5, 2) Example 1

5 of 7 Pre-Calculus2 Chapter 10 Section 8 Quadratic 2

6 of 7 Pre-Calculus2 Chapter 10 Section 8 Solve the system of equations Use elimination. Rewrite first equations. 3y 2 = 12 y 2 = 4 y = ±2 Example 2 y = –2 and y = 2. x 2 + 4(–2) 2 = 25 x 2 + 4(2) 2 = 25 x = 25 x 2 = 9 x = ± 3 (–3, 2) (–3, –2)(3, 2) (3, –2)

7 of 7 Pre-Calculus2 Chapter 10 Section 8 Graph the solutions for the systems on inequalities: and Graph the solutions for the systems on inequalities: and The first one is a parabola and the second one is an ellipse. Both boundaries are dashed lines. The first one is a parabola and the second one is an ellipse. Both boundaries are dashed lines. Example 3

8 of 7 Pre-Calculus2 Chapter 10 Section 8Practice Solve the system algebraically, then graphically :

9 of 7 Pre-Calculus2 Chapter 10 Section 8 Graph the solutions to the system of inequalities. Graph the solutions to the system of inequalities. Practice