Solve the given equation using elimination method: ax + by = a - b & bx - ay = a + b

Question

A test developed in 1924 by R.L. Smith & G.E. Sandland at Vickers Ltd as an alternative to the Brinell method, is used to measure what?

Answer 1

a[ax + by = a - b]  -- multiply by a 
b[bx - ay = a + b]  -- multiply by b
--------------------  adding two equations 
(a^2 + b^2)x  = a^2 + b^2
or 
x = 1 

now putting it in eq1
a + by = a - b 
or 
y = -1 

Answer
x=1 and y = -1