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Equations with Swapped Coefficients

Solve ax + by = c, bx + ay = d by adding and subtracting

The Rule

  1. 1Spot that the coefficients of x and y swap between the two equations.
  2. 2Add the equations and divide: this gives x + y.
  3. 3Subtract the equations and divide: this gives x − y.
  4. 4Add those two results and halve to get x; then find y.