Answer
The values are
$ a=3 $
and $ b=2 $.
Work Step by Step
The given equations are
$ ax-by=4 $ ... (1)
$ bx+ay=7$ ... (2)
If $ (2,1) $ is a solution of the systems than it must satisfy both equations.
The equation (1) will become
$ a(2)-b(1)=4 $
$ 2a-b=4 $
Isolate $ b $
$ b=2a-4 $ ... (3)
The equation (2) will become
$ b(2)+a(1)=7 $
$ 2b+a=7 $
Substitute the value of $b$ from equation (3).
$ 2(2a-4)+a=7 $
$ 4a-8+a=7 $
$ 5a-8=7 $
$ 5a=7+8 $
$ 5a=15 $
$ a=\frac{15}{5} $
$ a=3 $ Substitute into equation (3).
$ b=2(3)-4 $
$ b=6-4 $
$ b=2$.
