Question

Which point on the graph is a solution to the simultaneous inequalities y≤13x+2
and y<23x+4
?

(1 point)
Responses

(−10,−2)
left parenthesis negative 10 comma negative 2 right parenthesis

(2,5)
left parenthesis 2 comma 5 right parenthesis

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis

(−6,0)

Answer 1

To determine which point is a solution to the given simultaneous inequalities \( y \leq 13x + 2 \) and \( y < 23x + 4 \), we'll substitute each point into both inequalities.

1. **Point \((-10, -2)\)**:
- For \( y \leq 13x + 2 \):
\[
-2 \leq 13(-10) + 2 \implies -2 \leq -130 + 2 \implies -2 \leq -128 \quad \text{(false)}
\]

2. **Point \((2, 5)\)**:
- For \( y \leq 13x + 2 \):
\[
5 \leq 13(2) + 2 \implies 5 \leq 26 + 2 \implies 5 \leq 28 \quad \text{(true)}
\]
- For \( y < 23x + 4 \):
\[
5 < 23(2) + 4 \implies 5 < 46 + 4 \implies 5 < 50 \quad \text{(true)}
\]

3. **Point \((-4, -2)\)**:
- For \( y \leq 13x + 2 \):
\[
-2 \leq 13(-4) + 2 \implies -2 \leq -52 + 2 \implies -2 \leq -50 \quad \text{(false)}
\]

4. **Point \((-6, 0)\)**:
- For \( y \leq 13x + 2 \):
\[
0 \leq 13(-6) + 2 \implies 0 \leq -78 + 2 \implies 0 \leq -76 \quad \text{(false)}
\]

The only point that satisfies both inequalities is **(2, 5)**.

Thus, the solution is:
\[
(2, 5)
\]