# B How to Properly Use Substitution

#### FAS1998

When substitution is properly used for a set of equations, I believe you get a new equation with solutions that are also solutions of both of the previous equations.

The following equation has solutions x = 0 and x = 1.

$x=x^2$

This next equation has solutions x = -2 and x = 2.

$x^2=4$

but if we replace x^2 (in the second equation) with x from the first equation, we get the equation

$x=4$

which is incorrect. I believe correct use of substitution would should that there are no solutions to the system of equations.

Why is this substitution incorrect, and when can we validly substitute parts of one equation into another equation.

#### jedishrfu

Mentor
Normally when using substitution of one equation into another we solve for some varaible x and sub it in the second wherever x occurs.

It looks like you subbed for x^2 but not for x and you must do it for all the places where x occurs.

In this case subbing in $x=\sqrt 2$ too.

#### fresh_42

Mentor
2018 Award
I believe correct use of substitution would should that there are no solutions to the system of equations.
No! The correct way is not to use the same name for different things! You will not write banana on your list if you mean to buy apples. I cannot see why you do it here, and why we even discuss on this level!

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