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प्रश्न
Solve the following systems of linear inequations graphically:
x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
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उत्तर
Converting the inequations to equations, we obtain:
x\[-\]y=1, x +2y =8, 2x + y = 2, x = 0, y = 0
x\[-\] y = 1: This line meets the x-axis at (1, 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 \[-\]y ≤ 1 So, the portion containing the origin represents the solution set of the inequation x \[-\]y ≤ 1 x + 2y =8: This line meets the x-axis at (8, 0) and the y-axis at (0, 4). Draw a thick line joining these points.
We see that the origin (0, 0) satisfies the inequation x + 2y ≤ 8 So, the portion containing the origin represents the solution set of the inequation x + 2y ≤ 8
2x + y =2: This line meets the x-axis at (1, 0) and the y-axis at (0, 2). Draw a thick line joining these points.
We see that the origin (0, 0) does not satisfy the inequation 2x + y \[\geq\]2 So, the portion that does not contain the origin represents the solution set of the inequation 2x + y \[\geq\]2
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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