Substitution
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.
