which of the following points shows a solution to the simultaneous inequalities y > 1/2x + 5 and y < -2x + 1
(-1.6,4.2)
(4,8)
(1,5.5)
(-5,5)
To determine if a point is a solution to the simultaneous inequalities, we substitute the x and y values of the point into the inequalities and check if the inequalities hold true.
Let's check each of the given points:
1) Point (-1.6,4.2):
Substituting x = -1.6 and y = 4.2 into the inequalities:
4.2 > 1/2(-1.6) + 5
4.2 > -0.8 + 5
4.2 > 4.2 (True)
4.2 < -2(-1.6) + 1
4.2 < 3.2 + 1
4.2 < 4.2 (False)
Since the second inequality is not true, point (-1.6,4.2) is not a solution.
2) Point (4,8):
Substituting x = 4 and y = 8 into the inequalities:
8 > 1/2(4) + 5
8 > 2 + 5
8 > 7 (True)
8 < -2(4) + 1
8 < -8 + 1
8 < -7 (False)
Since the second inequality is not true, point (4,8) is not a solution.
3) Point (1,5.5):
Substituting x = 1 and y = 5.5 into the inequalities:
5.5 > 1/2(1) + 5
5.5 > 0.5 + 5
5.5 > 5.5 (False)
5.5 < -2(1) + 1
5.5 < -2 + 1
5.5 < -1 (False)
Since both inequalities are not true, point (1,5.5) is not a solution.
4) Point (-5,5):
Substituting x = -5 and y = 5 into the inequalities:
5 > 1/2(-5) + 5
5 > -2.5 + 5
5 > 2.5 (True)
5 < -2(-5) + 1
5 < 10 + 1
5 < 11 (True)
Since both inequalities hold true for point (-5,5), it is a solution to the simultaneous inequalities.
Therefore, the correct answer is (-5,5).