Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 42

Solve the system of equations $\begin{equation}
\begin{aligned}

4x + y - 2z =& 3 \\
\\
x + \frac{1}{4}y - \frac{1}{2}z =& \frac{3}{4} \\
\\
2x + \frac{1}{2}y - z =& 1

\end{aligned}
\end{equation}
$. If the system is inconsistent or has dependent equations, say so.

Multiplying each side of equation 2 by $4$ gives equation 1, so these two equations are dependent. Equation 1 and equation 3 are not equivalent, however, multiplying each side of equation 3 by $\displaystyle \frac{1}{2}$ does not give equation 1. Instead, we obtain two equations with the same coefficients, but with different constant terms. Thus, the system is inconsistent and the solution set is $\cancel{0}$.