Sūtra 6 of 16

Ānurūpyeṇa Śūnyamanyat

If one is in ratio, the other is zero

Used in solving simultaneous equations when coefficients of one variable are in ratio.

When to use

Two simultaneous linear equations where one variable's coefficients are proportional.

How it works

If the coefficients of one unknown are in the same ratio as the constants, the other unknown equals zero.

Memory formula

If one pair is proportional to the constants, the other unknown becomes zero.

Worked examples

Problem 1

6x + 7y = 8 ; 19x + 14y = 16

0/4

Code in your favourite language

When one variable’s pair is proportional to the constants, the other is zero.

Python

def anurupyena_shunyamanyat(a1, b1, c1, a2, b2, c2):
    if a1 * c2 == a2 * c1:  # x-coefficients proportional to constants
        return 0  # y = 0
    return None

print(anurupyena_shunyamanyat(2, 3, 4, 4, 5, 8))

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