SOLVING EQUATIONS

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SOLVING EQUATIONS

• CA 5.0

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Objective To create a foldable for the 6 steps
to solving equations
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Solving Equations Foldable
SOLVING EQUATIONS SYSTEMS SOLVING EQUATIONS SYSTEMS
Look for the DISTRIBUTIVE PROPERTY (distribute if necessary) Look for the DISTRIBUTIVE PROPERTY (distribute if necessary)
Look to COMBINE LIKE TERMS on the same side of the Equation Look to COMBINE LIKE TERMS on the same side of the Equation
Move the Variable Terms to the same side (use opposites) Move the Variable Terms to the same side (use opposites)
Undo the WEAK LINKS ADDITION/SUBTRACTION (use opposites) Undo the WEAK LINKS ADDITION/SUBTRACTION (use opposites)
Undo the STRONG LINKS MULTIPLICATION/DIVISION (multiply by reciprocal) Undo the STRONG LINKS MULTIPLICATION/DIVISION (multiply by reciprocal)
CHECK ? (use substitution order of operations) CHECK ? (use substitution order of operations)

LINEAR SYSTEMS
SPECIAL CASES
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Look for the DISTRIBUTIVE PROPERTY
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Look to COMBINE LIKE TERMS on the same side
6

Move the Variable Terms to the same side (use opposites)
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Undo the WEAK LINKS ADDITION/SUBTRACTION (use opposites)
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Undo the STRONG LINKS MULTIPLICATION/DIVISION (multiply by reciprocal)
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CHECK ? (use substitution)
?
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The SOLUTION to a linear system is the point of
intersection, written as an ordered pair. It is
also known as the BREAK EVEN POINT
? Possible Solutions of aLinear Equation
Result What Does This Mean? How Many Solutions?

• Ways to Solve a Linear System
• GRAPHING
• Time Consuming
• Estimate (not always accurate)
• Solution is the point of intersection
• SUBSTITUTION
• If a b and b c, then a c
• Best when both equations are in slope-intercept
  form
• ELIMINATION
• If a b and c d, then a c b d
• Best when both equations are in standard form

When the value of x is a, the equation is a true
statement.
Any value of x makes the equation a true
statement.
Infinitely Many
0 No Solution
There is no value of x that makes the equation a
true statement.
You can recognize a special case when ALL THE
VARIABLES DISAPPEAR
Result How Many Solutions? Graphically?



One Solution
Lines Intersect
Same Lines
Infinitely Many
No Solution
Parallel Lines
SPECIAL CASES
LINEAR SYSTEMS