Question

Which of the points on the graph is a solution to the simultaneous inequalities y≤14x+2
and y>12x+3
? Enter the x-value followed by the y-value.

Answer 1

To find a point on the graph that satisfies the simultaneous inequalities \( y \leq 14x + 2 \) and \( y > 12x + 3 \), we can test a few values of \( x \) in the inequalities.

1. **Choose a value for \( x \):**
Let's try \( x = 0 \).

- For \( y \leq 14(0) + 2 \):
\[
y \leq 2
\]

- For \( y > 12(0) + 3 \):
\[
y > 3
\]

So there is no \( y \) value that can satisfy both conditions simultaneously with \( x = 0 \).

2. **Choose another value for \( x \):**
Let’s try \( x = 1 \).

- For \( y \leq 14(1) + 2 \):
\[
y \leq 16
\]

- For \( y > 12(1) + 3 \):
\[
y > 15
\]

To satisfy both inequalities, \( y \) must be greater than 15 but less than or equal to 16. An example point would be \( (1, 15.5) \).

3. **Verifying the solution:**
- Is \( 15.5 \leq 16 \)? Yes.
- Is \( 15.5 > 15 \)? Yes.

Thus, the point \( (1, 15.5) \) is indeed a solution to the simultaneous inequalities.

The final answer is:

**1, 15.5**