Integrated Math 1 Extended - Unit 7 Name: __________________________
7.5A– Solving Systems Using Linear Combinations Date: _____________ Period: ______
Objective: To solve systems of linear equations by adding or subtracting to eliminate a variable
Warm up:
What is the solution to a system of equations?
VOCABULARY:
Linear Combinations: The process of solving a system of equations by multiplying one or both equations by a constant value (number) to get one of the variables to cancel out.
Solving System using LINEAR COMBINATIONS:
When solving a system of linear equations by linear combination…
1.) ______ or _____________ the equations to eliminate one variable
 When the coefficients of one variable are the same, multiply one of the equations by negative 1, so you get opposite signs
 When the coefficients of one variable are opposites, add the equations to eliminate the variable
(HINT: If you did the math correct, one variable should cancel out!!!)
2.) _________ the resulting equation
3.) _____________________ the value from Step 2 into one of the original equations
4.) Remember that you can _________ your answer by plugging your answers back into the equations

Example 1:
Solve the linear system using linear combination
A.) 4x + 2y = 12
-4x + 5y = 2
B.) 4x + 3y = 2
5x + 3y = -2
C.) 8x – 4y = -4
4y = 3x + 14
E.) 4x + 8y = 20
−4x + 2y = −30
D.) 2x + 3y = 11
-2x + 5y = -13
F.) −6x + 5y = 1
6x + 4y = −10

Integrated Math 1 Extended - Unit 7 Name: __________________________
7.5B– Solving Systems Using Linear Combinations Date: _____________ Period: ______
Objective: To solve systems of linear equations using linear combinations
Warm up:
Solve: x − y = 11
2x + y = 19
OH NO!!! What do I do if they aren’t the same number???
To eliminate one variable when adding or subtracting equations in a linear system,
______________ one or both equations by constants value (scalar)
Use the ________________________________ of the coefficients of one of the variables to determine the constants
Example 1:
Solve the linear system by using linear combination
A.) 6x + 5y = 19
2x + 3y = 5
B.) 4x + 5y = 35
-3x + 2y = -9

C.) 6x – 2y = 1
-2x + 3y = -5
D.) 2x + 5y = 3
3x + 10y = -3
Don’t Forget….
When solving a system of linear equations by linear combination…
 If you get an ________________, then the system has infinitely many solutions
 If you get a ___________ statement, then the system has no solution
Example 2:
How many solutions does each system have?
A.) 2x + 6y = 18 x + 3y = 9

B.) -2x + 5y = 7
-2x + 5y = 12
C.) 12x – 8y = 20
3x – 2y = 5
Example 3:
Solve the system of linear equations.
A.) Fred and Wilma are siblings, but they are not twins. This means that they are not the same age. Wilma is 4 years older than two times Wilma’s age. The sum of their ages is 19. How old is Fred and how old is Wilma?
B.) The sum of two numbers is 27. The larger number is 2 more than the smaller number. What are the two numbers?