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MathNet 2002 — Part 02 Question 74

Math Olympiad Vault · MathNet 2002 — Part 02

Question 74

The real numbers $x, y, z, w$ satisfy

$$
\begin{aligned}
2x + y + z + w &= 1 \\
x + 3y + z + w &= 2 \\
x + y + 4z + w &= 3 \\
x + y + z + 5w &= 25.
\end{aligned}
$$

Find the value of $w$.