Difference between revisions of "Substitution"
m (Added latex and fixed typo.) |
m |
||
| Line 12: | Line 12: | ||
<math>x+y=-1</math> Subtract <math>x</math> from both sides. | <math>x+y=-1</math> Subtract <math>x</math> from both sides. | ||
| + | |||
<math>y=-x-1</math> <math>y</math> is now isolated. | <math>y=-x-1</math> <math>y</math> is now isolated. | ||
| Line 17: | Line 18: | ||
<math>3x-(-x-1)=5 </math> Distribute the negative sign. | <math>3x-(-x-1)=5 </math> Distribute the negative sign. | ||
| + | |||
<math>3x+x+1=5</math> Combine like terms. | <math>3x+x+1=5</math> Combine like terms. | ||
| + | |||
<math>4x+1=5</math> Subtract 1 from both sides. | <math>4x+1=5</math> Subtract 1 from both sides. | ||
| + | |||
<math>4x=4</math> Divide both sides by four. | <math>4x=4</math> Divide both sides by four. | ||
| + | |||
<math>x=1</math> | <math>x=1</math> | ||
| Line 25: | Line 30: | ||
1+y=-1 Subtract 1 from both sides. | 1+y=-1 Subtract 1 from both sides. | ||
| + | |||
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.
