Concept 3.4
Elimination: Look for What Cancels
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
In the elimination method, multiply the equations by suitable non-zero constants so that the coefficients of one variable become numerically equal, then add or subtract the equations to eliminate that variable.
The intuition
Two equations are two true statements, so their sum is true too. If one variable has opposite coefficients, adding makes it vanish.
In 3x + 4y = 10 and 2x − 4y = 0, the y-terms are +4y and −4y. Add the equations: 5x = 10, so x = 2, and then y = 1.
The attention
Look for a variable whose coefficients already match in size.
3x + 4y = 10 2x − 4y = 0
Look hereNot here
- Look here
- Coefficients that match in size. +4y and −4y cancel when you add. That single observation decides the whole method.
- Not here
- The constants on the right. The constants change when you add, but they never decide what to do. They just come along for the ride.
- What it teaches
- Look for what cancels. Simplifying is mostly about spotting it.