Question
Solve graphically :2x – 5y ≥ 10
✓
Answer
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 2x = 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 J 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 nor equal to 10. ∴ 2x – 5y ≱ 10 in this 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.
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