-89./3

-104./3

Needs["VectorFieldPlots`"];

Clear[xmin,xmax,ymin,ymax]
xmin=-40.0;
xmax=3.0;
ymin=-50.0;
ymax=5.0;
Clear[axPlot];
axPlot=Plot[0,{x,xmin,xmax},PlotRange->{ymin,ymax}];

Clear[vecPlot];
vecPlot = VectorFieldPlot[{2x-2y-10,11x-8y+49},{x,xmin,xmax},{y,ymin,ymax}];
Show[axPlot,vecPlot]

Clear[xnull,ynull,equilGraphics]
xnull=Plot[x-5,{x, xmin, xmax},PlotStyle->{Red,Dashed,Thick}];
ynull = Plot[11/8x+49/8,{x, xmin, xmax},PlotStyle->{Blue,Dashed,Thick}];
equilGraphics = Graphics[{PointSize[Large],Point[{-89/3,-104/3}]}];
Show[{xnull, ynull, equilGraphics,axPlot,vecPlot},PlotRange->{{xmin,xmax},{ymin,ymax}}]

Det[{{-2,1},{1,-2}}]

Eigensystem[{{-2,1},{1,-2}}]

Solve[{-2x+y-21==0,x-2y+25==0}]

N[%]

Clear[xmin,xmax,ymin,ymax]
xmin=-10.0;
xmax=3.0;
ymin=-1.0;
ymax=15.0;
Clear[axPlot];
axPlot=Plot[0,{x,xmin,xmax},PlotRange->{ymin,ymax}];

Clear[vecPlot];
vecPlot = VectorFieldPlot[{-2x+y-21,x-2y+25},{x,xmin,xmax},{y,ymin,ymax}];
Show[axPlot,vecPlot]

Solve[-2x+y-21==0,y]

Solve[x-2y+25==0,y]

Clear[xnull,ynull,equilGraphics]
xnull=Plot[21+2x,{x, xmin, xmax},PlotStyle->{Red,Dashed,Thick}];
ynull = Plot[25/2+x/2,{x, xmin, xmax},PlotStyle->{Blue,Dashed,Thick}];
equilGraphics = Graphics[{PointSize[Large],Point[{-17/3,29/3}]}];
Show[{xnull, ynull, equilGraphics,axPlot,vecPlot},PlotRange->{{xmin,xmax},{ymin,ymax}}]

Clear[vecPlot];
vecPlot = VectorFieldPlot[{2x-2y-10,11x-8y+49},{x,xmin,xmax},{y,ymin,ymax}];
Show[axPlot,vecPlot]
Clear[xnull,ynull,equilGraphics]
xnull=Plot[21+2x,{x, xmin, xmax},PlotStyle->{Red,Dashed,Thick}];
ynull = Plot[25/2+x/2,{x, xmin, xmax},PlotStyle->{Blue,Dashed,Thick}];
equilGraphics = Graphics[{PointSize[Large],Point[{-17/3,29/3}]}];
Show[{xnull, ynull, equilGraphics,axPlot,vecPlot},PlotRange->{{xmin,xmax},{ymin,ymax}}]