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प्रश्न
Solve the following systems of inequations graphically:
5x + y ≥ 10, 2x + 2y ≥ 12, x + 4y ≥ 12, x ≥ 0, y ≥ 0
उत्तर
Converting the inequations to equations, we obtain:
5x + y = 10, 2x + 2y = 12, x + 4y = 12
5x + y =10: This line meets the x-axis at (2, 0) and y-axis at (0, 10). Draw a thick line through these points.
We see that the origin (0, 0) does not satisfy the inequation 5x + y\[\geq\]10
Therefore, the region that does not contain the origin is the solution of the inequality 5x + y\[\geq\]10
2x + 2y = 12: This line meets the x-axis at (6, 0) and y-axis at (0, 6). Draw a thick line through these points.
We see that the origin (0, 0) does not satisfy the inequation 2x + 2y\[\geq\]12
Therefore, the region that does not contain the origin is the solution of the inequality 2x+ 2y\[\geq\]12
x + 4y = 12: This line meets the x-axis at (12, 0) and y-axis at (0, 3). Draw a thick line through these points.
We see that the origin (0, 0) does not satisfy the inequation x + 4y\[\geq\]12
Therefore, the region that does not contain the origin is the solution of the inequality x + 4y\[\geq\]12Also, x ≥ 0, y ≥ 0 represents the first quadrant. So, the solution set must be in the first quadrant.
Hence, the solution to the inequalities is the intersection of the above three solutions. Thus, the shaded region represents the solution set of the given set of inequalities.
Here, the solution set is unbounded region.
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