Other Methods:  Vocabulary, Possible Solutions  Solver 
Graphically
By Linear Combination With Calculator 
Using Determinants
Using Matrices  
Substitution  Instructions  Problems w/Solutions 
Substitution means expression swapping. One expression is substituted or used in place of another expression of identical value so that a variable is eliminated.
Though this method always works, it is often easier to use another method unless one equations is already solved for one variable.
IF ONE EQUATION IS ALREADY SOLVED FOR ONE VARIABLE, use substitution.
Compare the two systems.


It's really the same system. The terms and format is just ordered differently.
The light blue one, on the left, is ideal for solution by substitution since one equations is already solved for one variable.
The light green one, on the right, is ideally set up for linear combination, or determinants.
Below the light blue one is solved by substitution.
So, to find the values of x and y, add lines together in a certain way.
Use Substitution to Solve Systems of Equations

Here's an example.
5x+4y=6  
y= 

5x+4  y  =6 
5x+4  ( )  =6 
5x+4(  2x+3  )=6 
5x+4(2x+3)=  6 
5x8x+12=  6 
3x+12=  6 
12  12 
3x=  6 
3x/(3)=  6/(3) 
x=  2 
y=  2x+3 
y=  2(x)+3 
y=  2( )+3 
y=  2(2)+3 
y=  4+3 
y=  1 
x = 2, y = 1 
(2, 1) 
Pick the systems best suited to solution by substitution.
If you picked correctly, "yes" is the message when you mouseover the 1st arrow. Solve the best suited systems for practice. A mouseover the 2nd arrow yields the solution to the system.  
x  2y = 2 3x  6y = 6 
y=4x  2 x=3 
5x + 5y = 10 10x + 10y = 12 
4x  3y=12 x=3y1 
4x+10y=22 y=3x9 
y = 2x + 4 y = 2x + 5 
y=4x+2 2y=8x+4 
y = 4x  1 8y = 8x + 8 
2x  2y = 4 3x  8y = 12 
x+3y=6 3x+9y=18 
4x + 4y = 10 x + y = 12 
y=x+2 y=4x+2 
2x +2y = 6 y=x+3 
3x+3y=6 6x+9y=12 
3x+ 3=y 9x3y=9 
5x+15y=10 3x+9y=6 