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.