Question
In the xy-plane, point A is contained in the graph of the solution set of the system of inequalities above. Which of the following could be the coordinates of point A?
- (2,1)
- (4,1)
- (4,5)
- (6,6)
Hint:
Hint:
We are given two inequalities in the xy-plane. We need to check if each of the co-ordinates given in the options satisfies the inequalities given in the question. If any one of the inequalities is not satisfied by the given co-ordinate, then A will not be that point.
The correct answer is: (4,5)
A) (2, 1)
Putting this point in the first inequality,
But this is not true as
.
Option A) is not correct
B) (4 , 1)
Putting this point in the first inequality,
But this is not true because 1 < 3
C) (4 , 5)
Putting this point in the first inequality,
This is true
Next, putting this point in the second inequality
This is also true.
Thus, we find that point (4, 5) satisfies both the given inequalities.
Hence, the point A is (4, 5)
The correct option is C)
Note:
An alternate way to find the solution is to plot the given inequalities in the xy-plane. Each inequality denotes either side of the line given by putting equal sign instead of the inequality. To find which side of the line satisfies the inequality, check with point (0, 0) and shade the region satisfied by the inequality. After that, check if each of the points given in the options satisfies the region shaded in the xy-plane.
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