Question

Four points and two intersecting lines are plotted on a coordinate plane. The x-axis ranges from negative 15 to 15 in unit increments, labeled at every 5. The y-axis ranges from negative 10 to 10 in unit increments, labeled at every 5.
Which of the points on the graph is a solution to the simultaneous inequalities y≤14x+2
and y>12x+3
? Enter the x-vavalue followed by the y-value.

(1 point)
(
,
)
Remaining Attempts : 3

Answer 1

To determine which of the points on the graph satisfies the simultaneous inequalities \(y \leq 14x + 2\) and \(y > 12x + 3\), we need to analyze the inequalities.

1. **Inequality 1: \(y \leq 14x + 2\)**
- This line (14x + 2) represents all points below and on the line.

2. **Inequality 2: \(y > 12x + 3\)**
- This line (12x + 3) indicates that we are looking for points above this line.

To find points that satisfy both inequalities, they must lie in the region where:
- They are below or on the line \(y = 14x + 2\).
- They are above the line \(y = 12x + 3\).

### Finding Points
Now, let's examine specific points \((x, y)\) one by one:

1. **Point 1 (for example, \((-5, -5)\):**
- Calculate for \(y = 14(-5) + 2 = -70 + 2 = -68\) (not satisfied)
- Calculate for \(y = 12(-5) + 3 = -60 + 3 = -57\) (not satisfied)

2. **Point 2 (for example, \((0, 0)\):**
- Calculate for \(y = 14(0) + 2 = 2\) (satisfied)
- Calculate for \(y = 12(0) + 3 = 3\) (not satisfied)

3. **Continue with other relevant points on the graph until one satisfies both inequalities.**

### Example Calculation
1. Check point \((1, 5)\):
- For \(y \leq 14x + 2 \implies 5 \leq 14(1) + 2 \implies 5 \leq 16\) (satisfied).
- For \(y > 12x + 3 \implies 5 > 12(1) + 3 \implies 5 > 15\) (not satisfied).

2. Check point \((1, 13)\):
- For \(y \leq 14x + 2 \implies 13 \leq 14(1) + 2 \implies 13 \leq 16\) (satisfied).
- For \(y > 12x + 3 \implies 13 > 12(1) + 3 \implies 13 > 15\) (not satisfied).

3. Check point \((2, 10)\):
- For \(y \leq 14x + 2 \implies 10 \leq 14(2) + 2 \implies 10 \leq 30\) (satisfied).
- For \(y > 12x + 3 \implies 10 > 12(2) + 3 \implies 10 > 27\) (not satisfied).

### Solution
Let's simplify and identify a point that satisfies both.

After further checking, you could denote a point through systematic checking until you locate \((x, y)\) aligned to the conditions described:

The point that works after thorough checking could potentially be something like:
\[
(x, y) = (x_0, y_0) \text{ satisfying both conditions.}
\]
Please replace \((x, y)\) here with your validated final coordinates based on which points you've verified satisfy both inequalities.

If necessary, please share specific points available on your graph for a targeted assessment!