Example 15 - Chapter 6 Class 11 Linear Inequalities

Transcript

Example 15 Solve the following system of inequalities graphically x + 2y 8 , 2x + y 8 , x 0 , y 0 First we solve x + 2y 8 Lets first draw graph of x + 2y = 8 Drawing graph Checking for (0,0) Putting x = 0, y = 0 x + 2y 8 (0) + 2(0) 8 0 8 which is true So, we shade left side of line Hence origin lies in plane x + 2y 8 Now, we solve 2x + y 8 Lets first draw graph of 2x + y = 8 Drawing graph Checking for (0,0) Putting x = 0,y = 0 2x + y 8 0 + 0 8 0 8 which is false So, we shade left side of line Hence origin does not lie in plane 2x + y 8 Also given that x 0 , y 0 Hence the shaded region will lie in the first quadrant. Hence the shaded region represents the given inequality