# Opposite Coefficients Method for Solving Two Equations in Two Unknowns

Opposite Coefficients Method for Solving Two Equations in Two Unknowns

This Demonstration solves the system of linear equations

ax+by=c

dx+ey=f

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 .)

x

d

-a

g=lcm(a,d)/a

h=-lcm(a,d)/d

lcm(a,d)

a

d

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

y

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

y

x