To determine which set of ordered pairs satisfies the given system of inequalities Y < 2X + 1 and X < 0, we need to check both inequalities for each point in the given sets. Let's go through each set of ordered pairs one by one:
### Set A: {(-1, 3), (-2, -5), (4, -8)}
1. **For point (-1, 3):**
- X < 0: Yes, -1 < 0.
- Y < 2X + 1: 3 < 2(-1) + 1 → 3 < -2 + 1 → 3 < -1 (False)
2. **For point (-2, -5):**
- X < 0: Yes, -2 < 0.
- Y < 2X + 1: -5 < 2(-2) + 1 → -5 < -4 + 1 → -5 < -3 (True)
3. **For point (4, -8):**
- X < 0: No, 4 < 0. (False)
Since not all points in Set A satisfy both inequalities, Set A is not the answer.
### Set B: {(-3, -2), (-2, 1), (-4, -8)}
1. **For point (-3, -2):**
- X < 0: Yes, -3 < 0.
- Y < 2X + 1: -2 < 2(-3) + 1 → -2 < -6 + 1 → -2 < -5 (False)
2. **For point (-2, 1):**
- X < 0: Yes, -2 < 0.
- Y < 2X + 1: 1 < 2(-2) + 1 → 1 < -4 + 1 → 1 < -3 (False)
3. **For point (-4, -8):**
- X < 0: Yes, -4 < 0.
- Y < 2X + 1: -8 < 2(-4) + 1 → -8 < -8 + 1 → -8 < -7 (True)
Since not all points in Set B satisfy both inequalities, Set B is not the answer.
### Set C: {(-1, -3), (-2, -5), (-4, -8)}
1. **For point (-1, -3):**
- X < 0: Yes, -1 < 0.
- Y < 2X + 1: -3 < 2(-1) + 1 → -3 < -2 + 1 → -3 < -1 (True)
2. **For point (-2, -5):**
- X < 0: Yes, -2 < 0.
- Y < 2X + 1: -5 < 2(-2) + 1 → -5 < -4 + 1 → -5 < -3 (True)
3. **For point (-4, -8):**
- X < 0: Yes, -4 < 0.
- Y < 2X + 1: -8 < 2(-4) + 1 → -8 < -8 + 1 → -8 < -7 (True)
All points in Set C satisfy both inequalities. Hence, Set C is the answer.
### Set D: {(-3, -2), (-2, -1), (-1, 3)}
1. **For point (-3, -2):**
- X < 0: Yes, -3 < 0.
- Y < 2X + 1: -2 < 2(-3) + 1 → -2 < -6 + 1 → -2 < -5 (False)
2. **For point (-2, -1):**
- X < 0: Yes, -2 < 0.
- Y < 2X + 1: -1 < 2(-2) + 1 → -1 < -4 + 1 → -1 < -3 (False)
3. **For point (-1, 3):**
- X < 0: Yes, -1 < 0.
- Y < 2X + 1: 3 < 2(-1) + 1 → 3 < -2 + 1 → 3 < -1 (False)
Since not all points in Set D satisfy both inequalities, Set D is not the answer.
Hence, the set of ordered pairs that satisfies the given system of inequalities is:
**C. {(-1, -3), (-2, -5), (-4, -8)}**
The graph below represents the following system of inequalities.
Y<2x+1
X<0
In a liner graph on a coordinate plane, A dotted line passes through (minus 4, minus 7), (minus 0.5, 0), (0, 1), and (3, 7) to form two shaded portions, white at the top and light gray at the bottom.
Which set of ordered pairs satisfy the given system of inequalities?
A.
{(-1,3), (-2,-5), (4,-8)}
B.
{(-3,-2), (-2,1), (-4,-8)}
C.
{(-1,-3), (-2,-5), (-4,-8)}
D.
{(-3,-2), (-2,-1), (-1,3)}
1 answer
2 answers