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Question
Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
Solution
Converting the inequations to equations, we obtain:
2x + 3y = 6, x + 4y = 4, 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
x + 4y = 4: This line meets the x-axis at (4, 0) and the y-axis at (0, 1). Draw a thick line joining these points.
We see that the origin (0,0) satisfies the inequation x + 4y ≤ 4.
So, the portion containing the origin represents the solution set of the inequation x + 4y≤ 4
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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