systems warm-up solve each linear system. 1.x + 7 = y -4x + 2 = y 2.x + 2y = 10 3y = 30 – 2x
TRANSCRIPT
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