Question

Solve the following inequation graphically in the two-dimensional plane.
`1/4 "x" + 1/2 "y" ≤ 1`

Answer 1

Given, inequation is `1/4 "x" + 1/2 "y" ≤ 1`

∴ corresponding equation is `"x"/4+"y"/2=1`
The two points required to plotting the line on the graph are

x	4	0
y	0	2

(4, 0) and (0, 2) on the X and Y are respectively.
Substitute x = 0, y = 0 in the inequation.
`1/4(0)+1/2(0)≤1`
i.e. 0 ≤ 1.
Origin satisfies the inequation on showing that the solution set contains the origin.
The solution set is towards the origin.