Question

solve the inequalities graphically
2x+3y<=12,x>=1,y>=2

Answer 1

Draw the line 3x+2y=12,x=1 and y=2. Now check for the position of origin w.r.t. the given lines to determine the solution of the inequalities.

For 3x+2y−12 at (0,0), 3(0)+2(0)−12<0. Hence, (0,0) lies in the inequality 3x+2y≤12

For x−1 at (0,0), 0−1<0. Hence, (0,0) doesn't lie in the inequality x≥1

For y−2 at (0,0), 0−2<0. Hence, (0,0) doesn't lie in the inequality y≥2.

The shaded part in the above graph represents the solution of the given inequlities.