Saṅkalana-Vyavakalanābhyām
By addition and by subtraction
Solving simultaneous equations by adding and subtracting them.
When the x and y coefficients are interchanged across two equations.
Add the equations to get one easy result, subtract them to get another. Particularly powerful when coefficients swap (like ax+by=p and bx+ay=q).
Add to remove one difficulty, subtract to remove the other.
Worked examples
Try it yourself
Try to solve, then reveal the steps one at a time.
Modern applications
Where this ancient technique still lives in today's world.
Add/subtract symmetry
Solving simultaneous equations by addition + subtraction is the core of Gaussian elimination — the most-used algorithm in numerical computing.
Code in your favourite language
Add and subtract symmetric equations to remove one unknown at a time.
def add_subtract(a, b, p, q):
# ax + by = p, bx + ay = q
s = (p + q) / (a + b) # x + y
d = (p - q) / (a - b) # x - y
return (s + d) / 2, (s - d) / 2
print(add_subtract(6, 7, 13, 13))Stuck? Ask the tutor.
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