Solve and analyze systems of equations by graphing and comparing tables.

Systems of Linear Equations  Two or more linear equations.  Any ordered pair that makes the system of linear equations true is called a solution of a system of linear equations. Must satisfy all equations in the system.  Can be used to model problems

Solving  There is more than one way to solve a system of equations.  One method is to graph both equations and find the intersection (if one exists)  EX: Find the solution to the system  The graphs intersect at the  point (2, 4) so that is the solution.

Checking  Substitute your solution into each equation and check that it makes each equation true.  Our solution was (2, 4) so:  It is the solution.

Using a Table  Press Y=  Enter the first equation in Y1 and the second in Y2  Now press 2 nd GRAPH (this will take you to TABLE)  Scroll up and down until you find where both Y1 and Y2 are equal.  Ex: -3x+2y=8 and x+2y= -8 Put into slope-intercept form first. (-4,-2)

Writing a System

Linear Regression  Find when the populations will be the same.  Go to 2 nd STAT (LIST) and enter the number of years since 1950 in L1, NY in L2, and LA in L3. Enter populations as millions and round to the nearest hundred thousand (12,911,994 as 12.9)  Now STAT→arrow right for CALC→LinReg(ax+b) For NY, type 2 nd 1(L1), 2 nd 2(L2) then ENTER and for LA type 2 nd 1(L1), 2 nd 3(L3) then ENTER This will find lines of best fit

Continued  Now graph both lines of best fit using Y=  Press 2 nd TRACE (CALC)→intersect  At the bottom it will say “First curve?” Make sure the cursor is on one line and press ENTER.  Now it will say “second curve?” Make sure the cursor is on the other line and press ENTER.  When it says “Guess?” press ENTER

Solutions

Types of Systems  A system that has at least one solution is consistent.  Consistent systems with exactly one solution are called independent.  Dependent systems are consistent and have infinitely many solutions.  If there is no solution, the system is called inconsistent.

Assignment  Odds p.138 #7-21