11.6 Solving Quadratic Systems

2 2

2 2

2 2

2

2

34

2

2 ( 2) 34 5 3

4 4 34 5 2 3 2

2 4 30 0 3 5

2 15 0

( 5)( 3) 0 ( 3, 5) (5,3)

5 3

x y

x y

x y y y y y

y y y x x

y y x x

y y

y y

y y

Two equations of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 considered together is called a quadratic system. You can have from 0 to 4 answers.

Ex 1) Identify, solve and graph

circle

line*substitution is the best method*

(–3, –5)

(5, 3)

2 2

2 2

2 2

2 2 2 2

2 2 2

2

2 2 2 2

172

2 3 6

2 17

2 3 6 2 2

2 4 34 8 17 8 17

7 28 9 9

4 3 3

2 ( 3,2) (3,2) ( 3, 2) (3, 2)

1 13 2 17

x y

x y

x y y y

x y x x

y x x

y x x

y

x y x y

Ex 2) Identify, solve and graph hyperbola

ellipse*addition is the best method*

–2 ( )

Ex 3) Determine two positive numbers whose sum is 17 and whose product is 72.

x + y = 17 x = 17 – y 0 = (y – 8)(y – 9) xy = 72 y = 8 y = 9

(17 – y)y = 72 x + 8 = 17 x + 9 = 17 17y – y2 = 72 x = 9 x = 8

0 = y2 – 17y + 72 8 and 9

Ex 4) Graph the system of inequalities2 2 2 2

2 2

16 9 1441

9 1636

x y x y

x y

circler = 6

Homework

#1108  Pg 574 #3, 7, 11, 13, 15, 18, 21, 25, 30, 33, 35, 37, 38, 43