vplot = VectorPlot[{x1+x2,4*x1+x2},{x1,-4,4},{x2,-4,4}, VectorScale->{0.04,1,None},Axes->True]

splot=StreamPlot[{x1+x2,4*x1+x2},{x1,-4,4},{x2,-4,4},PlotRange->{{-3,3},{-3,3}},Axes->True]

pplot1 = ParametricPlot[{t,2*t},{t,-3,3},PlotStyle->Black];

pplot2 = ParametricPlot[{t,-2*t},{t,-3,3},PlotStyle->Red];

Show[vplot,pplot1,pplot2]