शून्यम् साम्यसमुच्चये

Shūnyam Sāmyasamuccaye- “When the sum is the same, that sum is zero”

Solving algebraic equations

What Does It Mean?

This Vedic Math sutra simplifies equations where identical expressions appear on both sides. If the total (samuccaya) is the same (sāmya), it cancels out — leaving zero.

How It Works

  • Identify identical expressions or sums on both sides.
  • Cancel them out — the remaining part equals zero.
  • Solve the simplified equation.

Examples

Example 1

Equation: 7x + 3x = 4x + 6x
Both sides total to 10xx = 0

Example 2

Equation: 5(x + 1) = 3(x + 1)
Common factor (x + 1)x = -1

Why It’s Useful

Perfect for competitive exams, this sutra speeds up algebraic problem-solving and builds pattern recognition.