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Workbook

A linear inequality in two variables x and y is an inequality that can be written in one of the following
forms: ax by c, ax by c, ax by c,or ax by c        , Provided a and b are not both zero.

A solution to a linear inequality in two variables is an ordered pair that makes the inequality true. For

example, solutions to the inequality x y 6  are ordered pairs x,y such that the sum of the x-
and y- coordinates is less than 6. This inequality has an infinite number of solutions, and therefore it is
convenient to express the solution set as a graph.

PROCEDURE:

Step 1 : Solve for y, if possible.

Step 2 : Graph the related equation. Draw a dashed line if the inequality is strict, < or >. Otherwise,
draw a solid line.

Step 3: First choose any point from one of the two regions in the coordinate plane separated by the
graph of the equation. Then substitute the coordinates of this point into the inequality to see whether
it satisfies the inequality or not.

Step 4: If the point you have chosen satisfies the inequality then shade the region that the point
belongs to, otherwise shade the other region.

EXAMPLE 1: Graph the solution set. 3x y 1  

EXAMPLE 2: Graph the solution set. 4y 5x 

38 091math-wb-w6-(equations&inequalities-1)