Determine the value of $$ x $$ in the system of equations below $$ \begin{array}{l}x-2 y=5 \ 2 x-3 y=10 \ x=0 \ x=8 \ x=5 \ x=3\end{array} $$

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1. We begin with the given system of equations:
   $$
   \begin{aligned}
   x - 2y &= 5, \
   2x - 3y &= 10, \
   x &= 0, \
   x &= 8, \
   x &= 5, \
   x &= 3.
   \end{aligned}
   $$

2. First, note that the equations $$x=0$$, $$x=8$$, $$x=5$$, and $$x=3$$ are four separate statements for $$x$$ that cannot all be true simultaneously since $$x$$ cannot take on four different values at once. This indicates the full system is overdetermined and inconsistent.

3. However, if we focus on the first two equations:
   $$
   \begin{aligned}
   x - 2y &= 5, \
   2x - 3y &= 10,
   \end{aligned}
   $$
   we can solve for $$x$$ and $$y$$.

4. From the first equation, express $$x$$ in terms of $$y$$:
   $$
   x = 5 + 2y.
   $$

5. Substitute this expression for $$x$$ into the second equation:
   $$
   2(5+2y) - 3y = 10.
   $$

6. Simplify and solve for $$y$$:
   $$
   \begin{aligned}
   10 + 4y - 3y &= 10, \
   10 + y &= 10, \
   y &= 0.
   \end{aligned}
   $$

7. Substitute $$y=0$$ back into the expression for $$x$$:
   $$
   x = 5 + 2(0) = 5.
   $$

8. Thus, the solution to the first two equations is:
   $$
   (x, y) = (5, 0).
   $$

9. Notice that one of the additional equations is $$x=5$$, which agrees with the solution above, while the others ($$x=0$$, $$x=8$$, $$x=3$$) contradict it.

10. Conclusion: The overall system is inconsistent because it contains contradictory equations for $$x$$. If we only consider the pair of equations $$x-2y=5$$ and $$2x-3y=10$$, we obtain 
    $$
    x = 5.
    $$
The value of $$ x $$ is 5.

Determine the value of \( x \) in the system of equations below \( \begin{array}{l}x-2 y=5 \\ 2 x-3 y=10 \\ x=0 \\ x=8 \\ x=5 \\ x=3\end{array} \)

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