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§ 4.2
Solving Systems of Linear
Equations by Substitution

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*Sign up* Martin-Gay,
Beginning and Intermediate Algebra, 4ed
2
The Substitution Method
Another method (beside getting lucky with
trial and error or graphing the equations) that
can be used to solve systems of equations is
called the
substitution method
.
You solve one equation for one of the
variables, then substitute the new form of the
equation into the other equation for the solved
variable.

Beginning and Intermediate Algebra, 4ed
3
Solve the following system using the substitution method.
3
x
–
y
= 6
and
– 4
x
+ 2
y
= –8
Solving the first equation for
y
,
3
x
–
y
= 6
–
y
= –3
x
+ 6
Subtract 3
x
from both sides.
y
= 3
x
– 6
Multiply both sides by
–
1.
Substitute this value for
y
in the second equation.
–4
x
+
2y
= –8
–4
x
+ 2(3
x
– 6) = –8
Replace
y
with result from first equation.
–4
x
+ 6
x
– 12 = –8
Use the distributive property.
2

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