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Mr. Borosky
Section 3.2
3.2 Solve Linear Systems Algebraically p. 160-167
Algebra 2
Objective: 1. You will solve systems of linear equations algebraically.
ONLY COPY ONE OF THE VERSIONS EITHER THE BOOKS OR MR. BOROSKY’s
SUBSTITUTION METHOD
Steps Solving a Linear System by Substitution (Section 3.2)
1. Solve one of the equations for one of its variables
2. Substitute the expression from step 1 into the other equation and solve for
the other variable.
3. Substitute the value from step 2 into the revised equation from step 1 and
solve.
4. Check the solution in each of the original equations.
OR
Steps Solving a Linear System by Substitution (Mr. B. Version)
1. Pick an equation and solve it for one of the variables. Get one variable by
itself on the left and get everything else on the right.
2. Use the other equation and replace the variable with what was found in Step
1 and then solve for the 2nd variable.
3. Use the equation found in step 1 and then plug in the value found in step 2
to find the value of the other variable.
4. Check by plugging in x and y into the both equations.
ELIMINATION METHOD (LINEAR COMBINATION METHOD)
Steps for Solving a Linear System by Linear Combination (Section 3.2)
1. Arrange the like terms in columns. (if necessary)
2. Multiply if necessary, the equations by numbers to obtain coefficients that
are opposites for one of the variables. Remember you need OPPOSITE
Coefficients for one of the Variables.
3. Add the equations from step 2. Combining like terms with opposite
coefficients will eliminate one variable. Solve for the remaining variable.
4. Substitute the value obtained in step 3 into either of the original
equations and solve for the other variable.
5. Check the solution in each of the original equations.
OR
Steps for Solving a Linear System by Linear Combination (Mr. B. Version)
1. Arrange get x under x and y under y on the left and the #s are on the right.
(if necessary)
2. Find Opposite Coefficients for one of the variables. Multiply if necessary
to do this.
3. Add the equations from step 2. One variable becomes ZERO and Solve for the
remaining variable.
4. Pick an equation and plug in the value from step 3 to find the value of the
other variable.
5. Check by plugging in x and y into the both equations.
3.2 Solve Linear Systems Algebraically p. 160-167
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