Sankalana-Vyavakalanabhyam: Solve Systems in Seconds

"Sankalana-vyavakalanabhyam" means "By Addition and by Subtraction" and it's a wonderfully simple technique for a special type of simultaneous linear equations.

The "Addition-Subtraction" Rule ➕➖

This sutra is a lifesaver when you have two linear equations where the coefficients of 'x' and 'y' are interchanged. We just add and subtract the equations to get two very simple new equations.

Example

1. By Addition: (2x + 3x) + (3y + 2y) = (8 + 7) → 5x + 5y = 15, which simplifies to x + y = 3.
2. By Subtraction: (2x - 3x) + (3y - 2y) = (8 - 7) → -x + y = 1.
3. Solve: Now solve `x + y = 3` and `-x + y = 1`. This gives y = 2 and x = 1.