https://file.aiquickdraw.com/mathbot/file/1727035428773nslaaeji.jpg

Let's go through each problem from the image.

### Zadanie 12. (0–1)
You are asked to find which system of equations has more than one solution.

We need to check which system of linear equations is dependent or has infinitely many solutions. The given options are:

\[
A. \begin{cases} \frac{1}{2}x - \frac{1}{3}y = 1 \\ -3x + 2y = -6 \end{cases}
\]
\[
B. \begin{cases} x + 6y = 0 \\ 3x + y = 0 \end{cases}
\]
\[
C. \begin{cases} x - 6y = 3 \\ 6x - y = 3 \end{cases}
\]
\[
D. \begin{cases} 6x - 3y = 12 \\ 2x + y = -4 \end{cases}
\]

You need to check if the lines are parallel, identical, or intersect at one point.

### Zadanie 13. (0–3)
Given a polynomial \( W(x) = x^3 + px + q \), we are provided that \( W(2) = 32 \) and \( W(3) = 23 \). We are asked to find \( W(-1) \).

The equation can be set up using the conditions for \( W(2) \) and \( W(3) \), solving for \( p \) and \( q \), then substituting \( x = -1 \) to find \( W(-1) \).

### Zadanie 14. (0–1)
The function is given by \( f(x) = \frac{k}{\sqrt{3} - 7} \cdot x - 2 \), where \( k < 4 \). The task is to determine whether the function is:
- A. Increasing (\( f(x) \) is increasing if the coefficient of \( x \) is positive)
- B. Constant
- C. Decreasing (\( f(x) \) is decreasing if the coefficient of \( x \) is negative)

And then choose one of the justifications (1, 2, or 3) based on the value of \( k/\sqrt{3} - 7 \).

### Zadanie 15. (0–1)
The functions are given as:
\[
f(x) = \frac{1}{3}x + 1, \quad g(x) = -3x + 11
\]
We know that the graphs of these functions intersect at point \( P \). You need to find the coordinates of the intersection point \( P \) by solving the system:
\[
f(x) = g(x)
\]

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Would you like me to solve all the tasks or focus on a specific one?

Rozwiąż zadania 12, 13, 14, i 15 z obrazka.

This page provides solutions for linear equations, polynomial evaluations, and determining the intersection points of functions. It includes step-by-step explanations for problems involving systems of equations, polynomial evaluation at given points, and function behaviors based on slope and coefficients.

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