ax+ay+1=1

Solution for ax+ay+1=1 equation:

Simplifying
ax + ay + 1 = 1

Reorder the terms:
1 + ax + ay = 1

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

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

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

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

Solving
ax + ay = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(x + y) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1x' to each side of the equation.
x + -1x + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + y = 0 + -1x
y = 0 + -1x
Remove the zero:
y = -1x

Add '-1y' to each side of the equation.
y + -1y = -1x + -1y

Combine like terms: y + -1y = 0
0 = -1x + -1y

Simplifying
0 = -1x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}