Difference between revisions of "Substitution"
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Start with <math>x+y=-1</math>. | Start with <math>x+y=-1</math>. | ||
| − | x+y=-1 | + | <math>x+y=-1</math> Subtract <math>x</math> from both sides. |
| − | y=-x-1 y is now isolated. | + | <math>y=-x-1</math> <math>y</math> is now isolated. |
| − | Substitute (-x-1) for the y in 3x-y=5. | + | Substitute <math>(-x-1)</math> for the y in <math>3x-y=5.</math> |
| − | 3x-(-x-1)=5 | + | <math>3x-(-x-1)=5 </math> Distribute the negative sign. |
| − | 3x+x+1=5 Combine like terms. | + | <math>3x+x+1=5</math> Combine like terms. |
| − | 4x+1=5 Subtract 1 from both sides. | + | <math>4x+1=5</math> Subtract 1 from both sides. |
| − | 4x=4 Divide both sides by four. | + | <math>4x=4</math> Divide both sides by four. |
| − | x=1 | + | <math>x=1</math> |
x is now solved for, so substitute x into one of the original equations. | x is now solved for, so substitute x into one of the original equations. | ||
Revision as of 21:49, 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
(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.
