|
When we used the Addition
Method to solve a system of
equations, we still had to
do a substitution to solve
for the remaining variable.
With the substitution method,
we solve one of the equations
for one variable in terms
of the other, and then substitute
that into the other equation.
This makes more sense with
an example:
Example:
|
2y + x = 3 |
(1) |
|
4y – 3x = 1 |
(2) |
Equation 1 looks like it
would be easy to solve for
x, so we take it and
isolate x:
|
2y + x = 3 |
|
|
x = 3
– 2y |
(3) |
Now we can use this result
and substitute 3 - 2y in for x in equation 2:
Now that we have y,
we still need to substitute
back in to get x. We
could substitute back into
any of the previous equations,
but notice that equation 3
is already conveniently solved
for x:
And so the solution is (1, 1).
As a rule, the substitution
method is easier and quicker
than the addition method when
one of the equations is very
simple and can readily be
solved for one of the variables. |
