Question

Which point on the graph is a solution to the simultaneous inequalities and
?
(1 point)
y ≤ x + 2
1
3
y < x + 4
2
3
(−10, −2)
(2, 5)
(−6, 0)
(−4, −2)

Answer 1

To determine which point on the graph is a solution to the simultaneous inequalities \(y \leq x + 2\) and \(y < x + 4\), we need to evaluate each given point against these inequalities.

1. **Point (-10, -2)**:
- Check \(y \leq x + 2: -2 \leq -10 + 2 \Rightarrow -2 \leq -8\) (False)
- Since it fails the first inequality, we can stop here.

2. **Point (2, 5)**:
- Check \(y \leq x + 2: 5 \leq 2 + 2 \Rightarrow 5 \leq 4\) (False)
- Since it fails the first inequality, we can stop here.

3. **Point (-6, 0)**:
- Check \(y \leq x + 2: 0 \leq -6 + 2 \Rightarrow 0 \leq -4\) (False)
- Since it fails the first inequality, we can stop here.

4. **Point (-4, -2)**:
- Check \(y \leq x + 2: -2 \leq -4 + 2 \Rightarrow -2 \leq -2\) (True)
- Check \(y < x + 4: -2 < -4 + 4 \Rightarrow -2 < 0\) (True)

Since both inequalities are satisfied by the point (-4, -2), the solution to the simultaneous inequalities is:

**(-4, -2)**