What is the Method of Elimination?
The Method of Elimination is a strategic algebraic process used to solve a pair of simultaneous linear equations containing two variables. Simultaneous equations are a set of two or more equations that share the same unknown values. Solving them means finding a single unique pair of values for the variables that makes both mathematical statements true at the exact same time.
Think of it like balancing scales or managing a sports trade. You have two unknowns—such as the price of a cricket bat and the price of a ball. To find their individual prices, you must temporarily remove one of the unknowns from the picture so you can focus entirely on solving for the remaining one.
We can achieve this elimination using two distinct techniques:
- Substitution Technique: You isolate one variable in terms of the other variable using the simpler equation of the two. Then, you plug this new expression into the second equation. This removes that variable entirely, leaving you with a basic one-variable equation.
- Addition/Subtraction Technique: You modify one or both equations by multiplying them by numerical constants so that the coefficients of one chosen variable become perfectly identical or opposite. Then, you add or subtract the entire equations to make that variable disappear.
Let us compare these two techniques side-by-side:
| Feature | Substitution Technique | Addition/Subtraction Technique |
|---|---|---|
| **Core Action** | Replace a variable with an equivalent algebraic expression. | Add or subtract full equations to cancel out a variable. |
| **Modification Step** | Expressing x in terms of y, or y in terms of x. | Finding a Lowest Common Multiple (LCM) to match coefficients. |