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प्रश्न
Solve the following systems of inequations graphically:
2x + y ≥ 8, x + 2y ≥ 8, x + y ≤ 6
उत्तर
Converting the inequations to equations, we obtain:
2x + y = 8, x + 2y = 8, x + y = 6
2x + y = 8: This line meets the x-axis at (4, 0) and y-axis at (0, 8). Draw a thick line through these points.
Now, we see that the origin (0, 0) does not satisfy the inequation 2x + y \[\geq\]8.
Therefore, the region that does not contain the origin is the solution of the inequality 2x+ y\[\geq\]8x + 2y = 8: This line meets the x-axis at (8, 0) and y-axis at (0, 4). Draw a thick line through these points.
Now, we see that the origin (0, 0) does not satisfy the inequation x + 2y\[\geq\] 8
Therefore, the region that does not contain the origin is the solution of the inequality x + 2y 8
Therefore, the region that does not contain the origin is the solution of the inequality x + 2y\[\geq\]8
x + y = 6: This line meets the x-axis at (6, 0) and y-axis at (0, 6). Draw a thick line through these points.
Now, we see that the origin (0, 0) satisfies the inequation x + y\[\leq\] 6 Therefore, the region containing the origin is the solution of the inequality x + y\[\leq\]6
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.
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