Opposite Coefficients Method for Solving Two Equations in Two Unknowns

This Demonstration solves the system of linear equations

,

with the opposite coefficient method.

Step 1: to eliminate , multiply the first equation by and the second by , and add the equations. Even better: multiply the first with and the second with . (Here means the least common multiple of and .)

Step 2: add equations and solve a new equation for .

Step 3: substitute the solution for into the first given equation, and solve the new equation for .