# Difference between revisions of "Substitution"

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<math>x+y=-1</math> Subtract <math>x</math> from both sides. | <math>x+y=-1</math> Subtract <math>x</math> from both sides. | ||

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<math>y=-x-1</math> <math>y</math> is now isolated. | <math>y=-x-1</math> <math>y</math> is now isolated. | ||

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<math>3x-(-x-1)=5 </math> Distribute the negative sign. | <math>3x-(-x-1)=5 </math> Distribute the negative sign. | ||

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<math>3x+x+1=5</math> Combine like terms. | <math>3x+x+1=5</math> Combine like terms. | ||

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<math>4x+1=5</math> Subtract 1 from both sides. | <math>4x+1=5</math> Subtract 1 from both sides. | ||

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<math>4x=4</math> Divide both sides by four. | <math>4x=4</math> Divide both sides by four. | ||

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<math>x=1</math> | <math>x=1</math> | ||

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

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y=-2 | y=-2 | ||

− | (x,y)=(1,-2) | + | <math>(x,y)=(1,-2)</math> |

You can check this answer by plugging x and y into the original equations. | 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. | This same method is used for simultaneous equations with more than two equations. |

## Revision as of 21:57, 22 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 .

Subtract from both sides.

is now isolated.

Substitute for the y in

Distribute the negative sign.

Combine like terms.

Subtract 1 from both sides.

Divide both sides by four.

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

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

y=-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.