Question
Solve graphically :x + 2y ≤ 6
✓
Answer
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.
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