You might be tempted to try to divide the matrices, e.g. #X = B/A# where #B = ((4,5),(5,-1))# and #A=((-5,5),(-2,5))#. But actually, whenever you want to divide matrices, you instead turn the problem into matrix multiplication. In particular, to solve #AX = B#, we instead solve #X = B * A^-1#.
So first we compute #A^-1#. The formula for the inverse of a #2x2# matrix is:
#((a,b),(c,d))^-1 = 1/(ad-bc)((d,-b),(-c,a))#
That gives us:
#((-5,5),(-2,5))^-1 = 1/((-5*5)-(5*-2))((5,-5),(2,-5))#
#=-1/15((5,-5),(2,-5))#
#=((-1/3,1/3),(-2/15,1/3))#
Now we multiply #B * A^-1#:
#((4,5),(5,-1)) * ((-1/3,1/3),(-2/15,1/3))#
#=((-2,3),(-23/15, 4/3))#
