ax+by+1=0

Solution for ax+by+1=0 equation:

Simplifying
ax + by + 1 = 0

Reorder the terms:
1 + ax + by = 0

Solving
1 + ax + by = 0

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + ax + -1 + by = 0 + -1

Reorder the terms:
1 + -1 + ax + by = 0 + -1

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

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

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

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

Divide each side by 'x'.
a = -1x-1 + -1bx-1y

Simplifying
a = -1x-1 + -1bx-1y

Reorder the terms:
a = -1bx-1y + -1x-1