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Question
Solve the following systems of linear inequations graphically:
2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0
Solution
Converting the inequations to equations, we obtain:
2x + 3y = 35, x = 0, y = 0
2x + 3y = 35: This line meets the x-axis at (17.5, 0) and the y-axis at (0, 35/3). Draw a thick line joining these points.
We see that the origin (0, 0) satisfies the inequation 2x + 3y ≤ 35 So, the portion containing the origin represents the solution set of the inequation 2x + 3y ≤ 35
x = 2: This line is parallel to the x-axis at a distance 2 units from it.
We see that the origin (0, 0) does not satisfy the inequation x\[\geq\] 2 So, the portion that does not contain the origin represents the solution set of the inequation x\[\geq\]2
y = 3: This line is parallel to the y-axis at a distance 3 units from it.
We see that the origin (0, 0) does not satisfies the inequation y ≥ 3 So, the portion opposite to the origin represents the solution set of the inequation y ≥ 3
Clearly, x ≥ 0, y ≥ 0 represents the first quadrant.
Hence, the shaded region in the figure represents the solution set of the given set of inequations.
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