आनुरूप्ये शून्यमन्यत्
Ānurūpye Śūnyamanyat
"If one is in ratio, the other is zero"
What this sutra solves
Crack a two-variable system instantly when one variable’s coefficients are in a simple ratio.
Two combo deals at a counter give 3x+4y=11 and 6x+2y=10, where x and y are item prices.
x-coefficients 3 and 6 are in ratio 1:2 → scale and subtract → x = 1, y = 2.
Two equations, two unknowns. Instead of substituting, look for one variable whose coefficients line up in a simple ratio.
Read the two equations
Two equations, two unknowns. Instead of substituting, look for one variable whose coefficients line up in a simple ratio.
⚡ Speed Advantage
See how few steps Vedic method needs!
Best for
- • Simultaneous equations with ratio structure
Use when
- • Coefficients of one variable form a ratio between the two equations
Avoid when
- • General simultaneous equations (use Sankalana-vyavakalanabhyam)
Intuition
In simultaneous equations, if the ratio of coefficients matches, one variable vanishes and the other solves directly.
Story Mode
The Vanishing Variable
Two equations. Two unknowns. But look closely — one variable hides in plain sight behind a proportionality mask. When you spot the ratio, one variable simply disappears, and the problem becomes trivial.
Vedic vs conventional
multiply, subtract, solve — 4 steps.
ratio spotted → direct answer.
Applications
Simultaneous equations with proportional coefficients
Two equations where one variable's coefficients are proportional.
Common Mistakes to Avoid
Comparing constants instead of matching coefficient ratios
Wrong approach
Correct approach
Why this happens
💡 Students look at the whole equation instead of isolating the coefficient pattern.
Eliminating the wrong variable
Wrong approach
Correct approach
Why this happens
💡 The phrase "the other is zero" can be misread as a direct value rather than an elimination cue.
Why It Works
Start with two linear equations:
If one set of coefficients is proportional:
Scale and subtract to eliminate that variable:
The ratio tells you which variable can be removed immediately, reducing two equations to one simple equation.
When two equations have coefficients in the same ratio for one variable, subtracting the scaled equations eliminates it. The remaining variable is found in one step.