Let's carefully analyze the given system of equations:
[tex]\[
\begin{array}{l}
y = -1 \\
y = -3 \\
y = 1 \\
y = 3
\end{array}
\][/tex]
Here we have four equations, each giving a different value for [tex]\( y \)[/tex]:
1. [tex]\( y = -1 \)[/tex]
2. [tex]\( y = -3 \)[/tex]
3. [tex]\( y = 1 \)[/tex]
4. [tex]\( y = 3 \)[/tex]
For a system of equations to have a consistent solution, all equations must be satisfied by the same value of [tex]\( y \)[/tex]. However, in this system:
- The first equation states [tex]\( y = -1 \)[/tex],
- The second equation states [tex]\( y = -3 \)[/tex],
- The third equation states [tex]\( y = 1 \)[/tex],
- The fourth equation states [tex]\( y = 3 \)[/tex].
It is impossible for [tex]\( y \)[/tex] to be simultaneously [tex]\(-1\)[/tex], [tex]\(-3\)[/tex], [tex]\(1\)[/tex], and [tex]\(3\)[/tex] at the same time. These values are mutually exclusive and contradict each other.
Hence, this system of equations does not have a consistent or unique solution. In other words, there is no single value of [tex]\( y \)[/tex] that satisfies all four equations simultaneously.
Thus, the conclusion is:
There is no consistent solution for [tex]\( y \)[/tex].
