3.3 Solving Linear Systems by
Linear Combinations
OBJECTIVE: SOLVE A SYSTEM OF
LINEAR EQUATIONS IN TWO VARIABLES
BY THE LINEAR COMBINATION METHOD.
What is the Linear Combination method?
 A linear combination of two equations is an equation
obtained by (1) multiplying one or both equations by
a constant, if necessary, and (2) adding the resulting
equations.
Using the Linear Combination Method
Multiply, if necessary, one or both equations by a
constant so that the coefficients of one of the
variables differ only in sign.
2. Add the revised equations from Step 1. Combining
like terms will eliminate one variable. Solve for the
remaining variable.
3. Substitute the value obtained in Step 2 into either
of the original equations and solve for the other
variable.
4. Check the solution in each of the original
equations.
1.
Solve
x + y = -1
x–y=9
Solve
x + 2y = -11
3x - 2y = -1
Multiply One Equation
2x – 3y = 6
4x – 5y = 8
Solve
7x – 12y = -22
-5x + 8y = 14
No Solution
-4x + 8y = -12
2x – 4y = 7