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:

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: $x = \frac{16}{5}, \quad y = \frac{-9}{5}$

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