Name ________________________ Date _____________ Period _____
3.2 Solving Linear Systems Algebraically

There are two ways to solve linear systems algebraically
1. Substitution Method:
a. Solve one of the equations for one of its variables.
b. Substitute the expression from step “a” into the other
equation and solve for the other variable. You will get a
number answer here.
c. Substitute this number from step “b” back into the
revised equation from step “a” and solve. You will get a
number answer here too.
d. Write your ordered pair, (x,y).
2. Linear Recombination Method – adding equations to get rid of
one variable and solve for the other; then plug the one solved
for back into either of the original equations to solve for the
remaining variable
a. If necessary multiply one or both of the equations to
obtain coefficients that differ only in sign for one of the
variables.
b. Add the revised equations from step “a”. Combining like
terms will eliminate one of the variables. Solve for the
remaining variable.
c. Substitute the value obtained in step “b” into either of
the original equations and solve for the other variable.

Solve the following linear systems using the substitution method and
then solve using the linear recombination method:
3x + 4y = -4
x + 2y = 2
Linear System:
Solve using Substitution Method:
Solve using Linear Combination Method:
Final Answer:
(
,
)
2x – 4y = 13
4x – 5y = 8
Linear System:
Solve using Substitution Method:
Solve using Linear Combination Method:
Final Answer:
(
,
)
Linear System:
-2x + y = 6
4x – 2y = 5
Solve using Substitution Method:
Solve using Linear Combination Method:
Final Answer:
(
Linear System:
,
)
7x + 2y = -3
-14x – 4y = 6
Solve using Substitution Method:
Solve using Linear Combination Method:
Final Answer:
(
Linear System:
,
)
x – 2y = 3
2x – 4y = 7
Solve using Substitution Method:
Solve using Linear Combination Method:
Final Answer:
(
Linear System:
,
)
7x – 12y = -22
-5x + 8y = 14
Solve using Substitution Method:
Solve using Linear Combination Method:
Final Answer:
(
,
)