Paper test question cordinate geometry involving inequality

alternatively - just plug in:

if you do that, values for (x, y) satisfies for all quadrants but IV.

for ex: if x = 1 and y = -1
2x - 3y = 2+3 = 5 which is greater than -6.

any +ve value for x and -ve value for y donot satisfy the inequality 2x - 3y =< - 6.

LESSON - The General Objective of this lesson is to study linear inequalities.

PERFORMANCE OBJECTIVES - At the end of this lesson the student will be able to graph linear inequalities in two variables.

Linear Inequalities in Two Variables - Linear inequalities can be graphed almost the same way we graph linear equations. Consider the example from the previous section. The graph of the equation

2x - 3y = 6


Every point on the line satisfies the equation

2x - 3y = 6



This means that if you choose any point in the region above or below the line, those points will satisfy one of the following inequalities.

2x - 3y > 6

or

2x - 3y 6 .

Step 1 - Solve the related equality for y.

Step 2 - Determine two points by choosing suitable values for x. Let x = 0 and 3. Then y equals -2 and 0 respectively.
Step 3 - Locate these points A(0,-2), B(30) and draw a straight line through them, completely dividing the plane into two regions.
Step 4 - Choose the test point (0,0) and substitute it into the original inequality, to see if it satisfies the inequality.
If it does, the region the test point is in, is the solution.
If it doesn't, the region the test point is not in, is the solution.
2(0) - 3(0) = 0 > 6 No.

Therefore the solution is the region below the line -

2x - 3y = 6.