Chapter 3

By: elisa guzman &

Gavi diaz

What?

Solve systems by graphing Solve systems by substitution By elimination By linear programming Inequalities by graphing 3 by 3 equations

Words You Need To Know

System- two or more equations or inequalities

Solution to a system- intersection points Linear programming- a method used by

businesses and government to manage resources and time.

Cheat sheet

One solution- system name: independent, picture name: intersecting

No solution- system name: inconsistent, picture name: parallel

Infinitely Many Solutions- system name: dependent, picture name: consistent

Ways to know

Elimination

Substitution

graphing

3 by 3 equations

4 2 10

2(2 3 33)

4 6 66

4 2 10

4 76

19

4 2 19 10

4 38 10

4 28

7

7,19

x y

x y

x y

x y

y

y

x

x

x

x

6 3 36

12 2 48 2 / 2 12 48 / 2 6 24

6 3( 6 24) 36

6 18 72 36

12 36

3

6 3 24

5

3,5

x y

x y y x y x

x x

x

x

x

y

y

2 6 1

2

1

2.125, .5, .625

x y z

x y z

x y z

y 3x 4

y 3x 2

Ways to know

Inequalities by graphing

Linear programming

4 6

2 4

y x

y x

10 12p x y

Steps For solving a 3 by 3 equation

1) press 2nd and x-1 to pull up the matrix function 2) Go over to edit and press enter. To set the

matrix for a system of three variables with three equations, the numbers at the top of the screen should read 3x4. Change them if they do not say this. The first number represents the number of variables. The second number represents how many terms there are.

3) Type the coefficients from your system into the matrix making sure that you enter them alphabetically and that the solution to each equation is the last number on each line.

Steps Continued…

3) continued… Remember enter 0 if the variable is missing and 1 if there is not a number in front of the variable.

4) Press 2nd and mode to get to the main screen. Press 2nd and x-1 again. Go over to math and scroll up until your cursor is over “B: rref(“ Press enter to select it. Press 2nd and x-1 and select the first option 1: [A]. Press enter one more time.

5)Your answers will be the numbers in the last column. BUT watch out for special cases! If the bottom row has all 0’s then the answer is “infinitely many solutions”.

Steps Continued…

5)…If the bottom row has two 0’s, a 1 and another 0 then the answer is “no solution”.