MagicMath.com Logo

MagicMath Homepage
Middle School Homepage
More On Solving Linear Equations
Given two linear equations
a * X + b * Y = c    (1)

d * X + e * Y = f    (2)

The recommended solution procedure is
  1. Multiply equation (2) by -a, on both sides of course, and add the result to equation (1). The new equation, (3), you get has no X in it.
    (1) + -a * (2)     (3)

    This step eliminates one variable.
  2. Solve equation (3) you get for the value of Y.
  3. Plug the value of Y back into either equation (1) or equation (2), take your pick. You now get an equation, (4), with no Y in it.
  4. Solve equation (4) for the value of X.
  5. Now you have the solution.
Do You Know: The same variable elimination procedure can be applied to solve more then two linear equations with more then two variables. This leads to a topic in linear algebra.
algebra
Copyright © MagicMath Inc., Ohio USA, 2000
All rights reserved.