https://file.aiquickdraw.com/mathbot/file/1726160210765sje5y485.jpg

You have uploaded an image containing a set of algebraic equations. I will analyze and solve all the highlighted mathematical problems from the document.

Let's start by focusing on each highlighted section in the image:

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**First set of equations (Top left):**

1. \( \begin{cases} 
3x + 2y = 6 \\
4x + y = 11
\end{cases} \)

We can solve this system using substitution or elimination. I'll use substitution.

From the second equation, express \( y \) in terms of \( x \):

\[
4x + y = 11 \implies y = 11 - 4x
\]

Substitute this expression into the first equation:

\[
3x + 2(11 - 4x) = 6
\]
\[
3x + 22 - 8x = 6
\]
\[
-5x + 22 = 6
\]
\[
-5x = -16 \implies x = \frac{16}{5}
\]

Now substitute \( x = \frac{16}{5} \) back into \( y = 11 - 4x \):

\[
y = 11 - 4\left(\frac{16}{5}\right) = 11 - \frac{64}{5} = \frac{55}{5} - \frac{64}{5} = \frac{-9}{5}
\]

Thus, the solution to the first system is:
\[
x = \frac{16}{5}, \quad y = \frac{-9}{5}
\]

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**Second set of equations (Middle left):**

2. \( \begin{cases} 
2x - 3y = 1 \\
3x + 4y = 12
\end{cases} \)

We can again solve this by substitution or elimination. I'll use the elimination method here.

First, multiply the first equation by 4 and the second by 3 to align the coefficients of \( y \):

\[
4(2x - 3y) = 4

This problem focuses on solving systems of linear equations using both the substitution and elimination methods. Detailed solutions are provided for different sets of equations, with explanations suitable for students in Grades 8-10.

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