Question

Solve graphically : 2x – 5y ≥10

Answer 1

Consider the line whose equation is 2x – 5y = 10. To find the points of intersection of this line with the coordinate axes.
Put y = 0, we get x = 10, i.e. x = 5,
∴ A = (5, 0) is a point on the line.
Put x = 0, we get –5y = 10, i.e. y = –2
∴ B = (0, –2) is another point on the line.

Draw the line AB joining these points. This line divide the plane in two parts.
1. Origin side
2. Non-origin side
To find the solution set, we have to check the position of the origin (0,0) with respect to the line.
when x = 0, y = 0, then 2x – 5y = 0 which is neither greater non equal to 10.
∴ 2x – 5y `cancel>=`10 in the case.
Hence (0,0) will not lie in the required region.
Therefore, the given inequality is the non-origin side, which is shaded in the graph.
This is the solution set of 2x – 5y ≥10.