Substitution and elimination are two symbolic techniques used to solve linear equations. For example, if it is easy to set up an equation for substitution where 1 variable is on 1 side, then use that; For example, 4y=16+4x, you can easily divide by 4, get y=4+x (or y=x+4), and plug that into the other equation. In other cases where it may not be so easy
Fractions/decimals, etc., then you would probably rather use elimination.

1) The substitution method. This method is best utilized when one of the variables in one of the equations has a coefficient of 1 or -1, otherwise you will introduce fractions. Substitution can also be used for nonlinear systems of equations.
(2) Linear combinations also called the elimination method, multiplication and addition method, etc... My personal favorite as it can be done efficiently. It generalizes well to larger systems and is the underpinning of various other solution methods.
As the name implies it requires the equations to be linear.
You need to know both and be comfortable switching between them.

Can we get one for the elimination method too?
Also, can you solve the same problem using either of the two techniques?

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14-01-2015
Mathematics

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Substitution and elimination are two symbolic techniques used to solve linear equations. For example, if it is easy to set up an equation for substitution where 1 variable is on 1 side, then use that; For example, 4y=16+4x, you can easily divide by 4, get y=4+x (or y=x+4), and plug that into the other equation. In other cases where it may not be so easy
Fractions/decimals, etc., then you would probably rather use elimination.

1) The substitution method. This method is best utilized when one of the variables in one of the equations has a coefficient of 1 or -1, otherwise you will introduce fractions. Substitution can also be used for nonlinear systems of equations.
(2) Linear combinations also called the elimination method, multiplication and addition method, etc... My personal favorite as it can be done efficiently. It generalizes well to larger systems and is the underpinning of various other solution methods.
As the name implies it requires the equations to be linear.
You need to know both and be comfortable switching between them.

Can we get one for the elimination method too?
Also, can you solve the same problem using either of the two techniques?

Sagot :

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olemakpadu olemakpadu · Answer 1 · 2015-01-14T10:24:43-05:00

olemakpadu olemakpadu

14-01-2015

A simple sample problem for Elimination:

x - y = 1
x + y = 5

You can solve the same problem using either technique, as far the equations are linear equations.

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Sagot :

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