# Linear Algebra/Linear Geometry of n-Space

 Unique solution No solutions Infinitely many solutions ${\displaystyle {\begin{array}{*{2}{rc}r}\scriptstyle 3x&\scriptstyle +&\scriptstyle 2y&\scriptstyle =&\scriptstyle 7\\[-5pt]\scriptstyle x&\scriptstyle -&\scriptstyle y&\scriptstyle =&\scriptstyle -1\end{array}}}$ ${\displaystyle {\begin{array}{*{2}{rc}r}\scriptstyle 3x&\scriptstyle +&\scriptstyle 2y&\scriptstyle =&\scriptstyle 7\\[-5pt]\scriptstyle 3x&\scriptstyle +&\scriptstyle 2y&\scriptstyle =&\scriptstyle 4\end{array}}}$ ${\displaystyle \scriptstyle {\begin{array}{*{2}{rc}r}\scriptstyle 3x&\scriptstyle +&\scriptstyle 2y&\scriptstyle =&\scriptstyle 7\\[-5pt]\scriptstyle 6x&\scriptstyle +&\scriptstyle 4y&\scriptstyle =&\scriptstyle 14\end{array}}}$