Solve the system of equations: 2x = 8 - 3y 3x = y + 7

Let's solve the system of equations step by step:

The given system of equations is:

$$ \begin{cases} 2x = 8 - 3y \\ 3x = y + 7 \end{cases} $$

First, let's rearrange the equations to get them in a more standard form:

$$ \begin{cases} 2x + 3y = 8 \\ 3x - y = 7 \end{cases} $$

We can solve this system using the substitution or elimination method. Let's use the elimination method. Multiply the second equation by 3 to eliminate ( y ):

$$ 3(3x - y) = 3(7) \\ 9x - 3y = 21 $$

Now we have the following system:

$$ \begin{cases} 2x + 3y = 8 \\ 9x - 3y = 21 \end{cases} $$

Add the two equations to eliminate ( y ):

$$ (2x + 3y) + (9x - 3y) = 8 + 21 \\ 11x = 29 \\ x = \frac{29}{11} $$

Now that we have the value of ( x ), we can substitute it back into one of the original equations to find the value of ( y ). Let's use the second equation:

$$ 3x - y = 7 \\ 3(\frac{29}{11}) - y = 7 \\ \frac{87}{11} - y = 7 \\ y = \frac{87}{11} - 7 \\ y = \frac{87}{11} - \frac{77}{11} \\ y = \frac{10}{11} $$

So the solution to the system of equations is:

$$ x = \frac{29}{11}, \quad y = \frac{10}{11} $$

Answer: ( x = \frac{29}{11}, y = \frac{10}{11} )