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Topic
Solving Systems of
Equations Using
Elimination with Addition
and Subtraction.
Application
In the Math Bazaar, Carmela bought 3
packs of crackers and 4 packs of peanuts
and paid 27 pesos. Jane bought 3 packs of
the same crackers and 6 packs of the
same peanuts and paid 33 pesos. How
much does each pack of crackers and
peanuts cost?
Question
When do we used
elimination method by
addition and subtraction
in solving linear
systems?
Recall
Addition and Subtraction of Polynomials
3x
4y
+ -3x
- 4y
What can you say about adding opposite
terms?
What can you say about subtracting same
terms?
Recall
Addition and Subtraction of Polynomials
1.
3x + 2y = 6
+ 4x – 6y = 10
2.
-6x + 9y = 3
+ 5x – 11y = 12
Polynomials
+
5x – 6y = 12
8x + 6y = 15
-
3x + 7y = 1
3x – 2y = 19
3.
4.
Polynomials
5.
6.
5x – 6y = 14
2x – 6y = 3
8x + 2y = 16
+ 4x – 2y = 10
Solving Systems of Equations

Elimination means getting rid of
something, in this case, remove a
variable. Again, the idea is to have
only one variable to solve for.
 Elimination is easiest when the
equations are in standard form.
Solving a system of equations by elimination
using addition and subtraction.
Step 1: Put the equations in
Standard Form.
Step 2: Determine which
variable to eliminate.
Standard Form: Ax + By = C
Look for variables that have the
same coefficient.
Step 3: Add or subtract the
equations.
Solve for the variable.
Step 4: Plug back in to find
the other variable.
Substitute the value of the variable
into the equation.
Step 5: Check your
solution.
Substitute your ordered pair into
BOTH equations.
1) Solve the system using elimination.
x+y=5
3x – y = 7
Step 1: Put the equations in
Standard Form.
Step 2: Determine which
variable to eliminate.
Step 3: Add or subtract the
equations.
They already are!
The y’s have the same
coefficient.
Add to eliminate y.
x+ y=5
(+) 3x – y = 7
4x
= 12
x=3
1) Solve the system using elimination.
x+y=5
3x – y = 7
Step 4: Plug back in to find
the other variable.
Step 5: Check your
solution.
x+y=5
(3) + y = 5
y=2
(3, 2)
(3) + (2) = 5
3(3) - (2) = 7
The solution is (3, 2). What do you think the answer
would be if you solved using substitution?
2) Solve the system using elimination.
4x + y = 7
4x – 2y = -2
Step 1: Put the equations in
Standard Form.
They already are!
Step 2: Determine which
variable to eliminate.
The x’s have the same
coefficient.
Step 3: Add or subtract the
equations.
Subtract to eliminate x.
4x + y = 7
(-) 4x – 2y = -2
3y = 9
Remember to
“keep-changey=3
change”
2) Solve the system using elimination.
4x + y = 7
4x – 2y = -2
Step 4: Plug back in to find
the other variable.
Step 5: Check your
solution.
4x + y = 7
4x + (3) = 7
4x = 4
x=1
(1, 3)
4(1) + (3) = 7
4(1) - 2(3) = -2
Which step would eliminate a variable?
1.
2.
3.
4.
3x + y = 4
3x + 4y = 6
Isolate y in the first
equation
Add the equations
Subtract the equations
Multiply the first
equation by -4
Which step would eliminate a variable?
1.
2.
3.
4.
8x - y = 16
3x +y = 6
Isolate y in the first
equation
Add the equations
Subtract the equations
Multiply the first
equation by -2
Solve using elimination.
2x – 3y = -2
x + 3y = 17
1.
2.
3.
4.
(2, 2)
(9, 3)
(4, 5)
(5, 4)
Board Drill
Solve the system.
x+y=6
4x – y = 19
Answer
(5,1)
Board Drill
Solve the system
8x + 5y = 38
-8x + 2y = 4
Answer
(1,6)
Board Drill
3x + 4y = -6
-3x + 2y = 6
Answer
(-2,0)
Board Drill
x – y = 11
2x + y = 19
Answer
( 10 , -1 )
Board Drill
4x + 3y = 2
5x + 3y = -2
Answer
(-4,6)
Board Drill
5x – 2y = 24
3x + 2y = 24
Answer
(6,3)