13 of 1313 of 13 Items
07:45
Skip to resources
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 can substitute the x and y values into the original inequalities and see if they are true.
For the first inequality, y < 3x + 7:
- Substitute (1,10):
10 < 3(1) + 7
10 < 3 + 7
10 < 10
This is not true, so (1,10) is not a solution.
- Substitute (2,1):
1 < 3(2) + 7
1 < 6 + 7
1 < 13
This is true, so (2,1) is a solution.
- Substitute (4,3):
3 < 3(4) + 7
3 < 12 + 7
3 < 19
This is true, so (4,3) is a solution.
- Substitute (0,1):
1 < 3(0) + 7
1 < 0 + 7
1 < 7
This is true, so (0,1) is a solution.
- Substitute (-1,9):
9 < 3(-1) + 7
9 < -3 + 7
9 < 4
This is not true, so (-1,9) is not a solution.
- Substitute (1,3):
3 < 3(1) + 7
3 < 3 + 7
3 < 10
This is true, so (1,3) is a solution.
- Substitute (-2,1):
1 < 3(-2) + 7
1 < -6 + 7
1 < 1
This is not true, so (-2,1) is not a solution.
- Substitute (6,4):
4 < 3(6) + 7
4 < 18 + 7
4 < 25
This is true, so (6,4) is a solution.
Next, let's check the second inequality, y ≥ -2x + 5:
- Substitute (1,10):
10 ≥ -2(1) + 5
10 ≥ -2 + 5
10 ≥ 3
This is true, so (1,10) is a solution.
- Substitute (2,1):
1 ≥ -2(2) + 5
1 ≥ -4 + 5
1 ≥ 1
This is true, so (2,1) is a solution.
- Substitute (4,3):
3 ≥ -2(4) + 5
3 ≥ -8 + 5
3 ≥ -3
This is true, so (4,3) is a solution.
- Substitute (0,1):
1 ≥ -2(0) + 5
1 ≥ 0 + 5
1 ≥ 5
This is true, so (0,1) is a solution.
- Substitute (-1,9):
9 ≥ -2(-1) + 5
9 ≥ 2 + 5
9 ≥ 7
This is true, so (-1,9) is a solution.
- Substitute (1,3):
3 ≥ -2(1) + 5
3 ≥ -2 + 5
3 ≥ 3
This is true, so (1,3) is a solution.
- Substitute (-2,1):
1 ≥ -2(-2) + 5
1 ≥ 4 + 5
1 ≥ 9
This is not true, so (-2,1) is not a solution.
- Substitute (6,4):
4 ≥ -2(6) + 5
4 ≥ -12 + 5
4 ≥ -7
This is true, so (6,4) is a solution.
Based on these results, the points that are solutions to the system of inequalities are:
B) (2,1)
C) (4,3)
D) (0,1)
H) (6,4)