3-1 SOLVING SYSTEMS USING

TABLES AND GRAPHING

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 2nd 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

Alligator 1’s weight can be modeled by :

Alligator 2’s weight can be modeled by:

Solve by using a table(4, 10) so after 4 months, both will weigh 10 lbs

Linear Regression Find when the populations will be the same.

Go to 2nd 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 2nd 1(L1) , 2nd 2(L2) then ENTER and for LA type 2nd 1(L1) , 2nd 3(L3) then ENTER

This will find lines of best fit

Continued Now graph both lines of best fit using Y= Press 2nd 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