Since the point (-9,1) is a solution to the given system of equations, therefore, this point satisfies both equations.
For the first equation: ax + by = -31 a(-9) + b(1) = -31 -9a +b = -31 This can be rewritten as: b = -31 + 9a .............> equation I
For the second equation: ax - by = -41 a(-9) - b(1) = -41 -9a - b = -41 ...........> equation II
Substitute with equation I in equation II to get a as follows: -9a - b = -41 -9a - (-31 + 9a ) = -41 -9a + 31 - 9a = -41 -18a = -41-31 -18a = -72 a = 4
Substitute with the value of a in equation I to get b as follows: b = -31 + 9a b = -31 + 9(4) b = -31 + 36 b = 5
