Cool math fractal

math image

math image

pre-algebra help lessonsalgebra help lessonsprecalculus / calculus help lessonsmath anxiety survival guidegeometry math artmath and jigsaw puzzlesCoolmath booksother math stuff
math help lessonsmath practice problemsmath gamesmath dictionarygeometry trigonometry reference area
teacher's areaparent's areaCoolmath 4 kidsSpike's Game ZoneFinance FREAKTotally Stressed OutScience Monster
Coolmath Algebra
Systems of Equations 2x2's Lesson 5 - Systems of Inequalities
(page 3 of 4)
---- This algebra lesson explains how to solve systems of inequalities (linear programming).

math image
Now available: Coolmath Algebra books! Part 1, Part 2 and Part 3 covering the Algebra you need from Algebra 1 through Precalculus Algebra (Beginning Algebra through College Algebra)

other Coolmath Books: Coolmath Precalculus Review (the math you really need to survive Calculus 1) and Math Survival Guide (How to conquer math and deal with math anxiety)
line
Graphing Calculator Scientific Calculator << a new window will open for these
line

Ok, now let's do a system:

x + y is less than or equal to 3

x > -1

We just graph each one and see where they overlap.

the graph of x + y is less than or equal to 3 ... the portion of the graph under the line is shaded  the graph of x > -1 ... the portion of the graph to the right of the line is shaded

What will the intersection look like?

 

Knowing what this point is is going to be really important in the next section!

It LOOKS like it's (-1, 4), but we need to be sure.  Remember that the point of intersection is the solution to the system

stick the x = -1 into x + y = 3 for x

 a graph of x + y is less than or equal to 3 and x > -1 ... the shaded portion is to the right of the x = -1 and below x + y = 3

We have the x guy, so stick him into the other equation:

x + y = 3 ... -1 + y = 3 ... y = 4

Yep, the point is (-1, 4), so here's our official answer:

a graph ... the point of intersection of the two lines is ( -1 , 4 )
 

YOUR TURN:

Graph x + y < 4

x - y is greater than or equal to -2

 

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
line
Graphing Calculator Scientific Calculator << a new window will open for these
line

.....:::::::::::::::  HELP SUPPORT COOLMATH  :::::::::::::::.....
:::::::  link to us   :::::::   advertise with us  :::::::  why we have ads  :::::::

Thanks for visiting Coolmath.com
© 1997-2010 Coolmath.com, Inc.