Concept 3.3
Substitution: Pick the Easiest Door
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
In the substitution method, express one variable in terms of the other from one equation, and substitute it into the other equation, which then has only one variable.
The intuition
Substitution turns two unknowns into one. The work is easiest if you pick the variable that is already almost alone: one with coefficient 1.
In 2x + 3y = 11 and x − 2y = −12, the x in the second equation has coefficient 1. So x = 2y − 12, and the first equation becomes 2(2y − 12) + 3y = 11, giving y = 5 and x = −2.
The attention
Look for a variable with coefficient 1. Isolate that one.
2x + 3y = 11 x − 2y = −12
Look hereNot here
- Look here
- A variable with coefficient 1. x − 2y = −12 gives x = 2y − 12 straight away, with no fractions.
- Not here
- A variable with a bigger coefficient. Isolating the 2x gives x = (11 − 3y)/2: correct, but fractions slow everything down and invite slips.
- What it teaches
- Before you start, look for the easiest door in. Choosing well saves more time than working fast.