Solve a system of equation using the Gaussian elimination - High school Algebra I Exercises

Find the solutions of the following systems using Gaussian elimination.

\begin{cases} 2x+3y=2 \cr \cr 3x+2y=4 \end{cases}

\begin{cases} x= \dfrac{8}{5}\cr \cr y=-\dfrac{2}{5} \end{cases}

\begin{cases} x= \dfrac{4}{5}\cr \cr y=\dfrac{2}{5} \end{cases}

\begin{cases} x= 7\cr \cr y=-4 \end{cases}

This system has no solution.

\begin{cases} x-5y=-5 \cr \cr 3x+2y=19 \end{cases}

\begin{cases} x=2\cr \cr y=5\end{cases}

\begin{cases} x=2\cr \cr y=-5\end{cases}

\begin{cases} x=-2\cr \cr y=-5\end{cases}

This system has no solution.

\begin{cases} x-3y=5 \cr \cr -2x+6y=4 \end{cases}

\begin{cases} x=0 \cr \cr y=0 \end{cases}

\begin{cases} x=47 \cr \cr y=14 \end{cases}

\begin{cases} x=5 \cr \cr y=2 \end{cases}

This system has no solution.

\begin{cases} 4x-6y=10 \cr \cr 2x-3y=5 \end{cases}

\begin{cases} x= \dfrac{10+6t}{4} \cr \cr y=t \end{cases} where t \in \mathbb{R}

\begin{cases} x=2 \cr \cr y=-1 \end{cases}

\begin{cases} x= -1 \cr \cr y=3 \end{cases}

This system has no solution.

\begin{cases} x+y+z=3 \cr \cr 2x-y+5z=6 \cr \cr 4x+3y-8z=-1 \end{cases}

\begin{cases} x=1 \cr \cr y=1 \cr \cr z=1 \end{cases}

\begin{cases} x=-1 \cr \cr y=3 \cr \cr z=1 \end{cases}

\begin{cases} x=3 \cr \cr y=-1 \cr \cr z=1 \end{cases}

This system has no solution.

\begin{cases} x+6y-2z=4 \cr \cr 4x+2y-z=3 \cr \cr 2x+4y+z=0 \end{cases}

\begin{cases} x=\dfrac{1}{3} \cr \cr y=\dfrac{1}{6} \cr \cr z=-\dfrac{4}{3} \end{cases}

\begin{cases} x=\dfrac{1}{3} \cr \cr y=-\dfrac{1}{6} \cr \cr z=-\dfrac{4}{3} \end{cases}

\begin{cases} x=-\dfrac{1}{3} \cr \cr y=-\dfrac{1}{6} \cr \cr z=\dfrac{4}{3} \end{cases}

This system has no solution.

\begin{cases} 2x+2y-z=3 \cr \cr 4x+4y-2z=5 \cr \cr x+2y-z=1 \end{cases}

\begin{cases} x=0 \cr \cr y=1\cr \cr z=-1 \end{cases}

\begin{cases} x=0 \cr \cr y=-1\cr \cr z=-1 \end{cases}

\begin{cases} x=-1 \cr \cr y=0\cr \cr z=-1 \end{cases}

This system has no solution.