1. Algebra 2: 4.1 & 4.2
Brett Solberg AHS ‘11-’12

2. Warm-up Sit in your assigned seat and clear your desk. Pick up:
White Board
Marker
Eraser
Red Packet

3. Warm-up Graph the following lines on one big graph: y = 2x + 1
2x + 2y = 4
Where do these lines intersect?

4. Today’s Agenda Systems of Equations Graphing Substitution
Finding Solutions
Graphing
Substitution
Linear Combination

5. Activity How many solutions can 2 lines have? Graphing random lines
y = ( )x + ( )

6. Systems of Equations
System: Set of 2 or more equations.

7. Graphing to find Solutions
1) Solve both equations for y.
2)Graph the lines.
3) Identify where the lines intersect.
Example - Find the solution of:
y - 2x = 0 y + x = 3
y = 2x y = -x + 3

8. Substitution Javier Morales - RSL Sub of the Match
Substitution: Replacing a variable with what it is equal to.

9. Substitution 1) Solve for one variable. 2) Substitute 3)Solve
x = 4 2y + 3x = 16
2y + 3(4) = 16
2y = 4
y = 2

10. Examples 2x + y = 6 3x + 4y = 4 y = -2x + 6 3x + 4(-2x + 6) = 4

11. Linear Combination - Elimination
Eliminate a variable by combining statements.
Vertical Addition

12. Linear Combination - Elimination
-3x – 4y = -1
3x + 2y = 0
-3x + 3x – 4y + 2y = -1
-2y = -1
y = ½
3x + 2(½ ) = 0
3x = -1
x = -1/3

13. Linear Combination
One variable must have opposite coefficients to eliminate. You can alter equations to make elimination work. 2x + 3y = 6 -x – 2y = -4 -2x – 4y = -8 2x – 2x + 3y – 4y = -2 y = 2 -x – 2(2) = -4 x = 0

14. Linear Combination
Sometimes you need to alter both equations. 2x + 7y = 2 3x + 5y = -8 -6x – 21y = -6 6x + 10y = y = -22 y = 2 2x + 7(2) = 2 2x = -12 x = -6

15. Recap Graphing Substitution Linear Combination
Use if you have or can easily solve for y.
Substitution
Use if one variable can easily be solved for.
Linear Combination
Use if you can eliminate one variable easily.

16. Test Re-cap
2nd Period
Average 29/40 = 73%
High 42/42

17. Homework
4.1 pg 161 #2-14 even
4.2 pg 166 #1-20 all