The solution to the system of equations x + y = a − b and ax − by = a² + b² is:
A
x = a, y = b
B
x = a, y = −b
C
x = −a, y = b
D
x = −a, y = −b
Correct Option:
B
Explanation
Substitute x = a and y = −b into the first equation: x + y = a − b, which is satisfied. In the second equation, ax − by = a(a) − b(−b) = a² + b², which also matches exactly. Hence option B satisfies both equations.
