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Question
From the list below, select all of the points that are solutions to the system of inequalities.
{y<3x+7y≥−2x+5
Responses
A (1,10)(1,10)
B (2,1)(2,1)
C (4,3)(4,3)
D (0,1)(0,1)
E (-1,9)(-1,9)
F (1,3)(1,3)
G (-2,1)(-2,1)
H (6,4)
To determine which points are solutions to the system of inequalities, we need to check if each point satisfies both inequalities.
Let's start by checking each option:
A: (1,10)
For the first inequality, y < 3x + 7, we have 10 < 3(1) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 10 ≥ -2(1) + 5, which is true.
Therefore, (1,10) is a solution to the system of inequalities.
B: (2,1)
For the first inequality, y < 3x + 7, we have 1 < 3(2) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 1 ≥ -2(2) + 5, which is true.
Therefore, (2,1) is a solution to the system of inequalities.
C: (4,3)
For the first inequality, y < 3x + 7, we have 3 < 3(4) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 3 ≥ -2(4) + 5, which is true.
Therefore, (4,3) is a solution to the system of inequalities.
D: (0,1)
For the first inequality, y < 3x + 7, we have 1 < 3(0) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 1 ≥ -2(0) + 5, which is true.
Therefore, (0,1) is a solution to the system of inequalities.
E: (-1,9)
For the first inequality, y < 3x + 7, we have 9 < 3(-1) + 7, which is false.
Therefore, (−1,9) is not a solution to the system of inequalities.
F: (1,3)
For the first inequality, y < 3x + 7, we have 3 < 3(1) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 3 ≥ -2(1) + 5, which is true.
Therefore, (1,3) is a solution to the system of inequalities.
G: (-2,1)
For the first inequality, y < 3x + 7, we have 1 < 3(-2) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 1 ≥ -2(-2) + 5, which is true.
Therefore, (-2,1) is a solution to the system of inequalities.
H: (6,4)
For the first inequality, y < 3x + 7, we have 4 < 3(6) + 7, which is true.
For the second inequality, y ≥ -2x + 5, we have 4 ≥ -2(6) + 5, which is true.
Therefore, (6,4) is a solution to the system of inequalities.
Based on the above analysis, the solutions to the system of inequalities are:
A. (1, 10)
B. (2, 1)
C. (4, 3)
D. (0, 1)
F. (1, 3)
G. (-2, 1)
H. (6, 4)