Letβs try to solve the system of equations
\begin{equation*}
\begin{cases}
y \amp= 3x-1\\
5 \amp= -3x+y\\
\end{cases}
\end{equation*}
Since we already have \(y\) by itself in the first equation, we will plug that into the second equation:
\begin{align*}
5 \amp= -3x+y\\
5 \amp= -3x+(3x-1)\\
5 \amp= -3x + 3x - 1\\
5 \amp= -1
\end{align*}
When we tried to simplify this equation, both of the \(x\)βs canceled out, and we are left with a nonsense statement. Since \(5\) is never equal to \(-1\text{,}\) there is no way to make both equations true at the same time. Thefore, this system has no solution.