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Algebra II 200
Systems of Equations
Name__________________
Date_________
Systems of Equations
METHOD 3: Elimination
Part A: Addition and Subtraction
EXAMPLE: Solve the system of equations.
5x – y = 12
3x + y = 4
(If you were to add these 2 equations, which variable would cancel?)
EXAMPLE 2: Solve the system of equations.
6x + 7y = -15
6x – 2y = 12
(If you were to subtract these 2 equations, which variable would cancel?)
STEPS for ADDITION or SUBTRACTION ELIMINATION:
1) Add or subtract the equations in order to cancel one of the variables.
(It all depends on the coefficients and signs of each variable.)
2) Solve the resulting equation for the variable.
3) Use that answer to find the other variable by substituting it back into one of the
original equations.
4) Check your answers.
5) Write the answer as an ordered pair (x, y).
Algebra II 200
Systems of Equations
Name__________________
Date_________
PRACTICE: Solve the following problems by the addition-or-subtraction method.
1) 3x + 2y = 11
2x – 2y = 4
2) 3x + 2y = 19
3x – 5y = 5
Part B: Multiplication with Addition
**Multiplication is used for when the coefficients do not match up for one of the variables.
**Also used for when the coefficients are fractions.
EXAMPLE 1:
EXAMPLE 2:
4x – 5y = 23
3x + 10y = 31
3x + 4y = 2
5x + 9y = 1
EXAMPLE 3:
5
x y 7
3
y 7
x 
4 2
Algebra II 200
Systems of Equations
Name__________________
Date_________
PRACTICE: Solve the system of equations.
1)
4x – 5y =3
2)
x+y=5
3x
y6
2
4)
-2x + 4y = 6
-3x + 6y = 8
3x + 2y = -15
3)
5)
4x – 2y = 10
3x – y = 12
-3x + 5y = 7
6x – 10y = -14
6)
x
y9
2
y
x 8
2
Algebra II 200
Systems of Equations
Name__________________
Date_________
Homework:
7)
9)
6x  3y  6
8 x  5 y  12
8 x  3 y  5
10 x  6 y  13
8)
10)
2 x  y  1
3x  2 y  30
4x  2 y  5
2x  y  1