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

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

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

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

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

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

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

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

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

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

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

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

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

Linear Combination Sometimes you need to alter both equations. 2x + 7y = 2 3x + 5y = -8 -6x – 21y = -6 6x + 10y = -16 -11y = -22 y = 2 2x + 7(2) = 2 2x = -12 x = -6

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.

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

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