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

Solution for (a-b)x=(a+b)y equation:

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

Reorder the terms for easier multiplication:
x(a + -1b) = (a + b) * y
(a * x + -1b * x) = (a + b) * y
(ax + -1bx) = (a + b) * y

Reorder the terms for easier multiplication:
ax + -1bx = y(a + b)
ax + -1bx = (a * y + b * y)
ax + -1bx = (ay + by)

Solving
ax + -1bx = ay + by

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1ay' to each side of the equation.
ax + -1ay + -1bx = ay + -1ay + by

Combine like terms: ay + -1ay = 0
ax + -1ay + -1bx = 0 + by
ax + -1ay + -1bx = by

Add 'bx' to each side of the equation.
ax + -1ay + -1bx + bx = bx + by

Combine like terms: -1bx + bx = 0
ax + -1ay + 0 = bx + by
ax + -1ay = bx + by

Reorder the terms:
ax + -1ay + -1bx + -1by = bx + -1bx + by + -1by

Combine like terms: bx + -1bx = 0
ax + -1ay + -1bx + -1by = 0 + by + -1by
ax + -1ay + -1bx + -1by = by + -1by

Combine like terms: by + -1by = 0
ax + -1ay + -1bx + -1by = 0

The solution to this equation could not be determined.