Question

I need to know the description of the system of equations

Answer 1

Hello!

First, we have to solve this system, then we can classify it.

Let's solve:

`\begin{cases}4x+2y=-6 \\ 2x+y=8\end{cases}`

Let's isolate y in the second equation:

`y=8-2x`

Now, let's replace it in the first equation:

`\begin{gathered} 4x+2y=-6 \\ 4x+2\cdot(8-2x)=-6 \\ 4x+16-4x=-6 \\ \cancel{4x}+16\cancel{-4x}=-6 \\ 16=-6 \\ \text{FALSE!!!} \end{gathered}`

As we can see, this linear system has no solution.

Now, let's classify it:

As this does not admit any solution, we can say that it is inconsistent.