Sistema 2x2 gráficamente
Resuelve gráficamente el sistema de ecuaciones:
SOLUCIÓN
Resolución gráfica
Sistema de partida:
Forma explícita de cada recta:
Recta 1 (azul) — 
:
Recta 2 (roja) — 
:
Representamos las dos rectas y localizamos el punto de intersección:
![\begin{tikzpicture}
\begin{axis}[width=7cm,height=7cm,axis lines=center,xlabel=x,ylabel=y,
xmin=-11,xmax=11,ymin=-11,ymax=11,
xtick distance=2,ytick distance=2,
grid=both,grid style={line width=.2pt,draw=gray!30},
major grid style={line width=.4pt,draw=gray!60},
tick label style={font=\scriptsize},
legend style={font=\scriptsize,at={(0.02,0.98)},anchor=north west}]
\addplot[blue,very thick,domain=-11:11,samples=2]{(3-(2)*x)/(1)};
\addlegendentry{\(2x + y = 3\)}
\addplot[red,very thick,domain=-11:11,samples=2]{(9-(5)*x)/(1)};
\addlegendentry{\(5x + y = 9\)}
\addplot[only marks,mark=*,mark size=3pt,black] coordinates {(2,-1)};
\node[anchor=south west,font=\scriptsize,black] at (axis cs:2,-1) {\((2,-1)\)};
\end{axis}
\end{tikzpicture}](local/cache-TeX/735e6ad3e707cbd6c323ad471630d05b.png "\begin{tikzpicture}
\begin{axis}[width=7cm,height=7cm,axis lines=center,xlabel=x,ylabel=y,
xmin=-11,xmax=11,ymin=-11,ymax=11,
xtick distance=2,ytick distance=2,
grid=both,grid style={line width=.2pt,draw=gray!30},
major grid style={line width=.4pt,draw=gray!60},
tick label style={font=\scriptsize},
legend style={font=\scriptsize,at={(0.02,0.98)},anchor=north west}]
\addplot[blue,very thick,domain=-11:11,samples=2]{(3-(2)*x)/(1)};
\addlegendentry{\(2x + y = 3\)}
\addplot[red,very thick,domain=-11:11,samples=2]{(9-(5)*x)/(1)};
\addlegendentry{\(5x + y = 9\)}
\addplot[only marks,mark=*,mark size=3pt,black] coordinates {(2,-1)};
\node[anchor=south west,font=\scriptsize,black] at (axis cs:2,-1) {\((2,-1)\)};
\end{axis}
\end{tikzpicture}")
Las dos rectas se cortan en un único punto — solución del sistema:
