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Question
Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
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Solution
Converting the inequations to equations, we obtain:
2x + 3y = 6, 3x + 2y = 6, x = 0, y = 0
2x + 3y =6: This line meets the x-axis at (3,0) and the y-axis at (0, 2). Draw a thick line joining these points.
We see that the origin (0, 0) satisfies the inequation 2x + 3y ≤ 6
So, the portion containing the origin represents the solution set of the inequation 2x + 3y ≤ 6
3x+2y =6: This line meets the x-axis at (2, 0) and the y-axis at (0, 3). Draw a thick line joining these points.
We see that the origin (0,0) satisfies the inequation 3x + 2y ≤ 6.
So, the portion containing the origin represents the solution set of the inequation 3x + 2y ≤ 6
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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