Section [2.6] Linear Equalities in Two Variables Tutorial



A Linear Equality can be written as:

Ax+By<C
Ax+By>C
Ax+ByC
Ax+ByC

An ordered pair is a solution of a linear equality if the inequality is true when the x and y values are plugged into the inequality.
Ex #1: (2,0) would be a solution for the inequality y<2x-3.

0<2x-3
0<4-3
0<1 TRUE

Ex #2: (1,7) would be a soulution for the inequality y5x+2.
75(1)+2
75+2
77 TRUE

The graph of an inequality in two variables is the graph of all solutions of the inequality. There is a boundary line of the inequality which divides the coordinate plane into two half planes which is a shaded region that contains the points that are solutions of the inequality, and an unshaded region that contains the points that are not solutions.

In order to graph an inequality, follow these steps:
1) Graph the inequality. Use a dashed line for < and/or > and a solid line for and/or .
2) To decide which side of the graph to shade, test a point (not on the line) to see if it is a solution to the inequality. Usually (o,o) is the easiest, so try it first.
3) Shade the region of the "true" solution side.

Ex #1: Graph the inequality x5.



-Use (0,0) as a test point
-05 TRUE, therefore you would shade the side that (0,0) is on.

Graphing Linear Inequalities in two variables
Ex #2: Graph the inequality y>2x



-Use (1,1) as a test because the graph goes through the point 0, therefore (0,0) cannot be used.
-1>2(1)
-1>2 FALSE Now you would shade the side without (1,1).


PRACTICE PROBLEMS

Please solve the following problems.

1. Is (1,3) a solution to the inequality y5x+2?
2. Is (2,4) a solution to the inequality 2x+y>8?

Graph the following inequalities in a coordinate plane.

3. x<7
4. y5x+3
5. y3x+8
6. y>9
7. 4x-2y8
8. 3x+12y<4