SOLUTION: Determine if the following statement is always true. If it is not, provide a counterexample. If the mathematical operation* is defined for all numbers x and y as 2x+3y, then the

Question 334297: Determine if the following statement is always true. If it is not, provide a counterexample. If the mathematical operation* is defined for all numbers x and y as 2x+3y, then the operation * is commutative.
Answer by tinbar(133) (Show Source): You can put this solution on YOUR website!
x*y=2x+3y
y*x=2y+3x
clearly x*y does NOT satisfy y*x, therefore it is no commutative
let x=4, y=5
then x*y=2(4)+3(5)=8+15=23
y*x=2(5)+3(4)=10+12=22
since x*y does not equal y*x, this counterexample shows this operation definition is not commutative.
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