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Equations

MTH005 Ch 2 Special Cases

Special CaseDescription
Conditional equation graphing solution set If the variable has no exponent, the graphs of the left & right sides of the equation intersect at one point (x, y); x is the estimated solution of the equation.
Contradiction equation solutin set Empty set
Identity equation solution set All Real numbers
Conditional equation definition True or false depending on the replacement for the variable
Contradiction equation definition False for all replacements of the variable
Identity equation definition True for all replacements of the variable
Conditional equation graph Graphs of the left & right sides of the equation intersect at one point
Contradiction eqution graph Graphs of the left & right sides of the equation appear to be parallel lines (parallel lines never intersect; therefore there is no solution)
Identity equation graph Graphs of the left & right sides of the equation coincide (lines that coincide share all points in common; therefore all real numbers are solutions)
Algebraic solution of a Conditional equation Variable equals a number, if the variable has no exponent
Algebraic solution a Contradiction equation The variable is eliminated when solving, & the resulting equation is false (number = different number)
Algebraic solution of an Identity equation The variable is eliminated when solving, & the resulting equation is true (number = same number).
TI-83+ or 84+ table for a Conditional eqation If the variable has no exponent, there is only one value of x where Y1 and Y2 (values of the expressions) are equal (the same)
TI-83+ or 84+ table for a Contradiction equation Y1 and Y2 (values of the expressions) differ by the same amount for all values of the variable (x)
TI-83+ or 84+ table for an Identity equation Y1 and Y2 (values of the expressions) are the same for all values of the variable (x)
Meaning of x and y (x, y) x is the value of the variable when the equation is solved. y is the value of the expressions when the value of x is substituted for the variable and the resulting numeric expressions (left & right sides of the equation)are evaluated
Created by: powens