Which of the following does not show the Commutative Property? $$ \begin{array}{ll} ext { A. } b+y=y+6 & ext { B. } y x=x y \ ext { C. } x+y=y+x & ext { D. } x y=2=x y\end{array} $$

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Which of the following does not show the Commutative Property? $$ \begin{array}{ll}	ext { A. } b+y=y+6 & 	ext { B. } y x=x y \ 	ext { C. } x+y=y+x & 	ext { D. } x y=2=x y\end{array} $$

UpStudy AI · Accepted Answer

To determine which of the given options does not show the Commutative Property, we need to understand what the Commutative Property states. The Commutative Property applies to addition and multiplication, and it states that changing the order of the numbers does not change the result.

In mathematical terms:
- For addition: $$ a + b = b + a $$
- For multiplication: $$ a \cdot b = b \cdot a $$

Now, let's analyze each option:

**A.** $$ b + y = y + 6 $$  
This equation does not demonstrate the Commutative Property because it does not show that $$ b + y $$ equals $$ y + b $$. Instead, it compares $$ y + 6 $$ with $$ b + y $$, which is not relevant to the commutativity of addition.

**B.** $$ y x = x y $$  
This shows the Commutative Property of multiplication, as it states that $$ y \cdot x $$ equals $$ x \cdot y $$.

**C.** $$ x + y = y + x $$  
This shows the Commutative Property of addition, as it states that $$ x + y $$ equals $$ y + x $$.

**D.** $$ x y = 2 = x y $$  
This is a tautology and does not demonstrate the Commutative Property. It simply states that $$ x \cdot y $$ equals 2, but does not show the order of multiplication.

Based on this analysis, the option that does not show the Commutative Property is:

**A.** $$ b + y = y + 6 $$
Option A does not show the Commutative Property.

Which of the following does not show the Commutative Property? \( \begin{array}{ll}\text { A. } b+y=y+6 & \text { B. } y x=x y \\ \text { C. } x+y=y+x & \text { D. } x y=2=x y\end{array} \)

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