Saṅkalana-vyavakalanābhyāṃ — By addition and subtraction

संकलन-व्यवकलनाभ्याम् — Sankalana-vyavakalanabhyam

By addition and subtraction. Add the two equations to get one answer; subtract them to get another. Two equations → two answers in two steps.

Why it works: If ax+by=p and bx+ay=q, then adding: (a+b)(x+y)=p+q → x+y=(p+q)/(a+b). Subtracting: (a−b)(x−y)=p−q → x−y=(p−q)/(a−b). Then x and y follow from x=(sum+diff)/2.

Speed advantage: Symmetric equations solved in 2 steps instead of 6.

Best for

• Symmetric simultaneous equations

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Originally published at https://www.sutraflow.app/sutras/sankalana-vyavakalanabhyam