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Find the graphical solution of the following system of linear inequations:x60+y90≤1, x120+y75≤1, y ≥ 0, x ≥ 0 - Mathematics and Statistics

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Question

Find the graphical solution of the following system of linear inequations:
`"x"/60 + "y"/90 ≤ 1`, `"x"/120 + "y"/75 ≤ 1`, y ≥ 0, x ≥ 0

Sum
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Solution

Consider the equations:
`"x"/60 + "y"/90 ≤ 1`

x 60 0
y 0 90

The two points on the axes are (60, 0) and (0, 90) as in equation 60 and 90 are x and y-intercepts,
(x and y are equivalent to X and Y axes.)
∵ The inequation `"x"/60 + "y"/90 ≤ 1` satisfies the origin.
The solution set is towards the origin.
`"x"/120 + "y"/75 ≤ 1` 

x 120 0
y 0 75

The two points on the axes are (120, 0) and (0, 75) respectively.
The inequation `"x"/120 + "y"/75 ≤ 1` satisfies the origin.

The solution set of the inequation is towards origin x ≥ 0, y ≥0 are the inequations showing the conditions that the solutions set (common region) is in the first quadrant

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Chapter 8: Linear Inequations - Exercise 8.3 [Page 121]

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