Question

Ax + by = c, bx + ay = (1 + c)​

Answer 1

( x - y ) ( a - b ) = -1

Explanation:

ax + by = c and bx + ay = 1 + c

ax + by = c and bx + ay - 1 = c

And now we set c equivalent

ax + by = bx + ay - 1

ax - bx + by - ay = -1

x (a - b) + -y (a - b) = -1

(x - y) ( a - b) = -1

So we can leave it like that, or we can solve for one of the variables.

If we solve for y:

(x - y) ( a - b) = -1

(x - y) = -1 / (a - b)

-y = (-1 / (a - b)) - x

y = (1 / (a-b)) + x

Cheers.