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To do substitution, you must isolate one variable in one
of the equations, and then plug it into the other. The variable must be by
itself on one side of the equation, and it must have a coefficient of one.
When one variable is isolated, you can plug in its value into the other
equation.
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 Substitution
can always be used to solve linear systems of equations, however it is not
always the best way. It is the easiest way when one of the variables already
has a coefficient of one. It would not be practical to use this method when
both variables have an "ugly" coefficient like a fraction or a whole number
other than one. For example, this system would not be a good candidate for
the substitution method.
2x + 3y = 12
1/2x + 2y = -2
However, this system would be:
6x + 3y = 18
y - 3x = 4
Great Example
Explanation
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Example:
6x + 3y = 18
y - 3x = 4
Step #1- isolate a variable (in this case,
y)
y = 3x + 4
 Step
# 2- plug in its value into the other equation & solve
6x + 3( 3x + 4) = 18
Distribute > 6x + 9x + 12 = 18
Simplify > 15x = 30
x = 2
 Step
# 3- plug in the solution into the original equation and solve
y = (3 × 2) + 4
y = 10
Point of
intersection of the two linear equations
Solution:
(2 , 10)
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