# Difference between revisions of "Substitution"

(Overview and Methods of Solving Simultaneous Equations with Substitution) |
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Example: | Example: | ||

− | Solve x+y=-1, 3x-y=5 for (x,y). | + | Solve <math>x+y=-1, 3x-y=5</math> for <math>(x,y)</math>. |

− | Start with x+y=-1. | + | Start with <math>x+y=-1</math>. |

x+y=-1 Subtact x from both sides. | x+y=-1 Subtact x from both sides. |

## Revision as of 16:20, 21 April 2018

Substitution is a relatively universal method to solve simultaneous equations. It is generally introduced in a first year high school algebra class. A solution generally exists when the number of equations is exactly equal to the number of unknowns. The method of solving by substitution includes:

1. Isolation of a variable 2. Substitution of variable into another equation to reduce the number of variables by one 3. Repeat until there is a single equation in one variable, which can be solved by means of other methods.

Example:

Solve for .

Start with .

x+y=-1 Subtact x from both sides. y=-x-1 y is now isolated.

Substitute (-x-1) for the y in 3x-y=5.

3x-(-x-1)=5 Distribute the negative sign. 3x+x+1=5 Combine like terms. 4x+1=5 Subtract 1 from both sides. 4x=4 Divide both sides by four. x=1

x is now solved for, so substitute x into one of the original equations.

1+y=-1 Subtract 1 from both sides. y=-2

(x,y)=(1,-2)

You can check this answer by plugging x and y into the original equations.

This same method is used for simultaneous equations with more than two equations.