Systems Warm-Up

Solve each linear system.1. x + 7 = y

-4x + 2 = y

2. x + 2y = 10 3y = 30 – 2x

Visualize all of the possible solutions to 2 lines

1 solution as an

Ordered pair

Infinitely man solutions—same line

No solution– Parallel Lines

Solving Systems of Linear and Quadratic Equations

8

10

2

x y

x y

Systems of Linear EquationsWe had 3 methods to solve them.

Method 1 - Graphing

Solve for y.

2 8y x

10y x (6, – 4)

Systems of Linear Equations

Method 2 - Substitution

8

10

2

x y

x y

2 8y x

10x y 10x 2 8x

2 8 10x x 3 18x

6x 6

2 8y x 2( ) 8y 12 8y 4y

(6, – 4)

Systems of Linear Equations

Method 3 - Elimination

2 8

10

x y

x y

2 8

10

x y

x y

3 18x

6x 6

10x y ( ) 10y 4y 4y

(6, – 4) All 3

methods

giving us the

same answer

(6,–4).

Visualize all of the possible solutions to a Line & a Parabola

1 solution as an

Ordered pair2 solutions No solution

Solve the System AlgebraicallyUse Substitution

1

12

xy

xy

1 xy( ) 1x

Answer: (0,1) (1,2)

2 1x

02 xx

1 0x x 0 1 0x or x 0 1x or x

0x

(0, 1)

1x

(1, 2)

Solve the System AlgebraicallyUse Substitution

2 2y x 2( ) 2 2x x 22 x

Answer: (2,2)

2 2 2y x x 2x

(2, 2)

22

222

xy

xxy

20 4 4x x 0 2 2x x

0 2x 2x

Homework

(BK) Pg 202, 8 – 16