Symmetric Property of Equality

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The Symmetric property of equality states that if first expression is equal to the second expression, then the second expression should also be equal to the first expression. Let ‘a’ and ‘b’ be any two expressions, then according to the symmetric property of equality, it can be stated as, if a = b, then b = a. This property is true because in an equation, the right side and the left side are equated, and hence it should be valid even if they are flipped around.
 
Example 1: Show the symmetric property of equality for the given equation, 3x+ 2y= 5x+ y when x= 1 and y= 2. 

In order to prove the symmetric property of equality, let’s take the right side and the left side expressions.

Right side: 3x + 2y when x= 1, y= 2==> (3* 1)+ (2* 2) = 3+ 4= 7

Left side: 5x+ y when x= 1, y= 2==> (5* 1)+ 2= 5+ 2= 7.

Since both the sides are equal, we can also say that 5x+ y = 3x+ 2y.
 
Example 2: Show the symmetric property of equality for the given equation, 2x– y = x+ 2y when x= 3 and y= 1.

In order to prove the symmetric property of equality, let’s take the right side and the left side expressions.

Right side: 2x- y when x= 3, y= 1==> (2* 3) – 1= 6- 1= 5.

Left side: x+ 2y when x= 3 and y= 1==> 3+ (2*1) = 3+ 2= 5.

Since both the sides are equal, we can also say that x+ 2y= 2x- y.
 
 

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