Solve equations
Crack a two-variable system when one variable’s coefficients are in ratio
Full elimination means scaling both equations and bookkeeping — but a visible ratio shortcuts it.
Spot it when
One variable’s coefficients across the two equations form a clean ratio (3 and 6, 2 and 4…).
Watch it solved
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!
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
A simultaneous-equations question gives 3x+4y=11 and 6x+2y=10 — the x-coefficients jump out as 1 : 2.
Scale the first by 2, subtract to kill x → y = 2, then x = 1.
Two combo deals at a counter encode the same kind of system; you want each item price.
Spot the proportional variable, eliminate it, read off the other in one division.
An exam system is built so one variable’s coefficients are an obvious multiple — a gift if you notice.
Match the proportional coefficient, subtract, and the other variable falls out at once.
The method behind it
आनुरूप्ये शून्यमन्यत्
Ānurūpye Śūnyamanyat
“If one is in ratio, the other is zero”
In simultaneous equations, if the ratio of coefficients matches, one variable vanishes and the other solves directly.
multiply, subtract, solve — 4 steps.
ratio spotted → direct answer.
Use when
- • Coefficients of one variable form a ratio between the two equations
Avoid when
- • General simultaneous equations (use Sankalana-vyavakalanabhyam)