Beauty in Symmetry

Algebra Level 3

\[ \begin{cases} x + y + z + 18a + b = 135802458 \\ x + y + 18z + a + b = 135802458\\ 18x + y + z + a + b = 135802458\\ x + 18y + z + a + b = 135802458\\ x + y + z + a + 18b = 135802458 \end{cases} \]

Solve the system of equations above for real values of \(x\), \(y\), \(z\), \( a\), \(b \).

Enter the value of \(x\) as your answer.

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