UPSC CDS Math Quadratic Equations and Inequations Questions

It can be seen that the shaded region and the origin are on the same side of the line 2x+6y=21.For (0,0),2×0+6×0−21<0.
So, the shaded region satisfies the inequality 2x+6y≤21. Also, the shaded region and the origin are on the same side of the line 5x−2y=10. For (0,0),5×0−2×0−10<0.So, the shaded region satisfies the inequality 5x−2y≤10.