Question

Solve the following system of inequalities graphically.
x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0

Answer 1

To find graphical solution, construct the table as follows:

Inequation	Equation	Double Intercept form	Points  (x, y)	Region
x + 2y ≤ 10	x + 2y = 10	`"x"/10 + "y"/5` = 1	A (10, 0), B (0, 5)	0 + 2(0) ≤ 10 ∴ 0 ≤ 10 ∴ origin side
x + y ≥ 1	x + y = 1	`"x"/1 + "y"/1` = 1	C (1, 0), D (0, 1)	0 + 0 `≱` 1 ∴ 0 `≱` 1 ∴ non-origin side
x – y ≤ 0	x – y = 0	–	0 (0, 0), E(1, 1)	0 – 0 ≤ 0 ∴ 0 ≤ 0 ∴ origin side
x ≥ 0	x = 0	–	–	R.H.S. of Y-axis
y ≥ 0	y = 0	–	–	Above X-axis

The shaded portion represents the graphical solution.