=-x+(a-2)y+1

Solution for =-x+(a-2)y+1 equation:

Simplifying
0 = -1x + (a + -2) * y + 1

Reorder the terms:
0 = -1x + (-2 + a) * y + 1

Reorder the terms for easier multiplication:
0 = -1x + y(-2 + a) + 1
0 = -1x + (-2 * y + a * y) + 1

Reorder the terms:
0 = -1x + (ay + -2y) + 1
0 = -1x + (ay + -2y) + 1

Reorder the terms:
0 = 1 + ay + -1x + -2y

Solving
0 = 1 + ay + -1x + -2y

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.
0 + -1ay = 1 + ay + -1x + -1ay + -2y
Remove the zero:
-1ay = 1 + ay + -1x + -1ay + -2y

Reorder the terms:
-1ay = 1 + ay + -1ay + -1x + -2y

Combine like terms: ay + -1ay = 0
-1ay = 1 + 0 + -1x + -2y
-1ay = 1 + -1x + -2y

Divide each side by '-1y'.
a = -1y-1 + xy-1 + 2

Simplifying
a = -1y-1 + xy-1 + 2

Reorder the terms:
a = 2 + xy-1 + -1y-1