Answer :
Point given in Option (A). (-5, 0) will be the solution of the given inequalities.
Calculations for the solution to system of inequalities:
- If a point (h, k) lies in the solution area of the inequalities, it will satisfy the inequalities.
Given inequalities are,
x² + y² ≤ 25 -------(1)
x < y² - 2 ------(2)
To find the points given in the options, satisfy the inequalities with the ordered pairs.
Option (A). For (-5, 0),
x² + y² ≤ 25
(-5)² + 0 ≤ 25
25 ≤ 25 [True]
x < y² - 2
-5 < (0) - 2
-5 < -2 [True]
Therefore, (-5, 0) will lie in the solution are of the inequalities.
Option (2). For (-2, 0),
x² + y² ≤ 25
(-2)² + 0 ≤ 25
4 ≤ 25 [True]
x < y² - 2
(-2) < (0) - 2
-2 < -2 [False].
Therefore, (-2, 0) will not lie in the solution area.
Option (3). (5, 0)
x² + y² ≤ 25
5² + 0 ≤ 25
25 ≤ 25 [True]
x < y² - 2
5 < 0 - 2
5 < -2 [False]
Therefore, (5, 0) will not lie in the solution area of the inequalities.
Option (4). (2, 2)
x² + y² ≤ 25
2² + 2² ≤ 25
8 ≤ 25 [True]
x < y² - 2
5 < 0 - 2
5 < -2 [False]
Therefore, (2, 2) will not lie in the solution area of the system of inequalities.
Hence, Option (A). (-5, 0) is the point lying in the solution area of the system of inequalities.
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