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 15:20, 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.
