2
@12 Solving by Elimination
%7
^1
Two or more equations with the same 
variables form a system of linear 
equations.  To solve such a system, 
find the ordered pair that makes both 
equations true.  
^2
Add all the members of the first 
equation to those of the second.  One 
variable is cancelled out so that a 
simple equation with only one variable 
remains.  
^3
Use the Multiplication Property to find 
the value of the variable.
^4
Substitute the value of this variable 
into the simpler of the two original 
equations.  
Find the value of the remaining 
variable.
^5
Use the Addition Property to isolate 
the variable term and simplify.
^6
Use the Multiplication Property to find 
the value of the remaining variable and 
simplify.
^7
Write the two values as an ordered pair 
(in alphabetical order).
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%9
^1
Two or more equations with the same 
variables form a system of linear 
equations.  To solve such a system, 
find the ordered pair that makes both 
equations true.
^2
In some equations, the coefficients of 
one variable do not cancel out.  
In this case, use the Multiplication 
Property to multiply equation(s) by a 
number(s) that will cause the 
coefficients to cancel.
^3
Simplify.
^4
Add the members of the first equation 
to those of the second, cancelling out 
one variable.
^5
A simple equation with only one 
variable remains.  Use the 
Multiplication Property to find its 
value.
^6
Substitute the value of this variable 
into the simpler of the two original 
equations.  Find the value of the 
remaining variable and simplify.
^7
Use the Addition Property to isolate 
the variable term and simplify.
^8
Use the Multiplication Property to find 
the value of the remaining variable and 
simplify.
^9
Write the two values as an ordered pair 
(in alphabetical order).
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@22 Solving by Substitution
%8
^1
The substitution method is another way 
to solve a system of linear equations.
^2
If a variable in one equation is 
isolated on one side of the equal sign, 
substitute the value of that variable 
into the other equation.
^3
Multiply.
^4
Collect like terms.
^5
Use the Multiplication Property and/or 
Addition Property to find the value of 
the variable.
^6
Substitute the value of this variable 
into the simpler of the two original 
equations to find the value of the 
remaining variable.
^7
Simplify.
^8
Write the two values as an ordered 
pair.
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%10
^1
The substitution method is another way 
to solve a system of linear equations.
^2
Select the simplest equation and use 
the Addition and/or Multiplication 
Property to isolate the single variable 
term. 
^3
Substitute the value of this variable 
into the other equation.
^4
Distribute.
^5
Collect like terms.
^6
Use the Addition Property to isolate 
the variable and simplify.
^7
Use the Multiplication Property to find 
the value of the variable and simplify.
^8
Substitute the value of this variable 
into the simpler of the original 
equations to find the value of the 
remaining variable.
^9
Simplify completely using the Addition 
and/or Multiplication Property.
^10
Write the two values as an ordered 
pair.
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