Question

Classify the system (options: consistent, independent consistent, inconsistent) 4x + 2y = 8y = -2x + 8

Answer 1

Write both equations in standard form:

$ax+by=c$

The first one is already written in standard form:

$4x+2y=8$

To write the second one in standard form, add 2x to both members of the equation:

$\begin{gathered} y=-2x+8 \\ \Rightarrow y+2x=-2x+8+2x \\ \Rightarrow2x+y=8 \end{gathered}$

Notice that if we divide both members of the first equation by 2, we get:

$\begin{gathered} \frac{4x+2y}{2}=\frac{8}{2} \\ \Rightarrow2x+y=4 \end{gathered}$

Then, the system of equations is equivalent to:

$\begin{gathered} 2x+y=8 \\ 2x+y=4 \end{gathered}$

For the transitive property of equality, since both left members are the same, we can conclude from that system of equations that 8=4, which is false. Then, the system is inconsistent, since it leads to a contradiction.

Therefore, the answer is:

$\text{Inconsistent}$