Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 36

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

& y = -4x \\
& 8x + 2y = 4

\end{aligned}
\end{equation}
$ by substitution. If the system is inconsistent or has dependent equations.

Since equation 1 is solved for $y$, we substitute $-4x$ for $y$ in equation 2.


$
\begin{equation}
\begin{aligned}

8x + 2(-4x) =& 4
&& \text{Substitute } y = -4x
\\
8x - 8x =& 4
&& \text{Multiply}
\\
0 =& 4
&&

\end{aligned}
\end{equation}
$


Combining the equations give, $0 = 4$ which is a false statement. There are no ordered pairs that satisfy both equations, so there is no solution for the system. Therefore, the system is inconsistent.