Question

Given the system of inequalties, select all answers that satisfy:

There are 2

x-y<3

x+y>2

a
(4,1)

b
(5,5)

c
(0,2)

d
(2,4)

Answer 1

To determine which points satisfy the system of inequalities given by \( x - y < 3 \) and \( x + y > 2 \), we can evaluate each option.

1. **Option a: (4, 1)**
- Check \( x - y < 3 \):
\[
4 - 1 = 3 \quad \text{(not less than 3, fails)}
\]
- Check \( x + y > 2 \):
\[
4 + 1 = 5 \quad \text{(satisfies)}
\]
- Result: **Does not satisfy the system.**

2. **Option b: (5, 5)**
- Check \( x - y < 3 \):
\[
5 - 5 = 0 \quad \text{(satisfies)}
\]
- Check \( x + y > 2 \):
\[
5 + 5 = 10 \quad \text{(satisfies)}
\]
- Result: **Satisfies the system.**

3. **Option c: (0, 2)**
- Check \( x - y < 3 \):
\[
0 - 2 = -2 \quad \text{(satisfies)}
\]
- Check \( x + y > 2 \):
\[
0 + 2 = 2 \quad \text{(not greater than 2, fails)}
\]
- Result: **Does not satisfy the system.**

4. **Option d: (2, 4)**
- Check \( x - y < 3 \):
\[
2 - 4 = -2 \quad \text{(satisfies)}
\]
- Check \( x + y > 2 \):
\[
2 + 4 = 6 \quad \text{(satisfies)}
\]
- Result: **Satisfies the system.**

### Summary of Results:
- Option **b (5,5)** satisfies the system.
- Option **d (2,4)** satisfies the system.

The answers that satisfy the system of inequalities are **b** and **d**.