I have a system of ordinary differential equations.
dx/dt=-x and
dy/dt=2x-2y

I am using StreamPlot to plot the phase portrait which gives me this
[![enter image description here](https://i.stack.imgur.com/Z9lQ4.png)](https://i.stack.imgur.com/Z9lQ4.png)

I want to pic some initial condition and study that whether the solution leads to the equilibrium point(stable one) or not. I am trying a lot but didn't getting the required result as in the picture below

[![enter image description here](https://i.stack.imgur.com/ZuBpd.png)](https://i.stack.imgur.com/ZuBpd.png)

I require the blue arrowed lines that are solid and pass through the equilibrium points ie (0,0) here in the pic.
Thanks in advance for the help.