Question

Solve graphically : x +2y ≤ 6

Answer 1

Consider the line whose equation is x +2y ≤ 6. To find the points of intersection of this line with the coordinate axes.
Put y = 0, we get x = 6.
∴ A = (6, 0) is a point on the line.
Put x = 0, we get 2y = 6, i.e. y = 3
∴ B = (0, 3) is another point on the line.

Draw the line AB joining these points. This line divide the line into 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 x + 2y = 0 which is less than 6.
∴ x + 2y ≤ 6 in this case.
Hence, origin lies in the required region. Therefore,the given inequality is the origin side which is shaded in the graph.
This is the solution set of x + 2y ≤ 6.