Question$\begin{array}{l}-5 x-y+2 z=4 \\ 4 x+9 y-5 z=-12 \\ 2 x-5 y+z=2\end{array}$

Studdy Solution
Verify the solution by substituting $x = 1$, $y = 1$, $z = 5$ into the original equations:
Equation 1: $-5(1) - 1 + 2(5) = 4$
$$-5 - 1 + 10 = 4$$
$$4 = 4$$ (True)
Equation 2: $4(1) + 9(1) - 5(5) = -12$
$$4 + 9 - 25 = -12$$
$$-12 = -12$$ (True)
Equation 3: $2(1) - 5(1) + 5 = 2$
$$2 - 5 + 5 = 2$$
$$2 = 2$$ (True)
The solution is verified: $x = 1$, $y = 1$, $z = 5$.
The solution is $\boxed{(x, y, z) = (1, 1, 5)}$.