Thread: finding equilibrium for a system of equations

I am having problems with a homework problem. I am told for a systems of the form ⃗x = A⃗x + ⃗b to find the equilibrium point. Our textbook does not cover this but my teacher did cover this in class but did not give an example how to do problems like this she just did did proofs with no numbers. I have attached the problem as a jpeg. I was able to find the eigenvalues for each matrix I just am lost in finding the equilibrium for the system. Any help would be appreciated.

Find the values of x and y for which the right side is zero. That's the equilibrium point. A phase portrait of the system is easily drawn in Mathematica:

Code:

eqPt =
 Graphics[{PointSize[0.01], Red, Point[{-1, 1/2}]}];
Show[{StreamPlot[{x + 1, 3 x + 2 y + 2}, {x, -5, 5}, {y, -5, 5}], 
  eqPt}]

thanks for the help! I was not fully understanding the problem because I though it was x instead of x prime. thanks!