Find the values of a and b so that the solution of the linear system is (−9, 1). ax+by=−31, ax−by=−41. show work

Since (-9, 1) is the solution of ax+by = -31 and ax-by = -41, (-9,1) should satisfy the equations.
Plug -9 and 1 in place of x and y in both the equations.
Therefore, -9a+b = -31 and -9a-b = -41

adding both equations you get,
-18a = -72
∴ a = 4

Plug a=4 in -9a+b = -31 to obtain b,
-9(4)+b = -31
b = -31+36 = 5
∴ b =5