Q:
# What is the symmetric property of equality?

**The symmetric property of equality states that if two variables a and b exist, and a = b, then b = a.** The symmetric property of equality is one of the equivalence properties of equality.

The symmetric property of equality allows individuals to manipulate an equation by flipping the statements on each side of the equals sign. For example, in algebra, this means that the equations 11 = 2x + 5 and 2x + 5 = 11 are equivalent.

One useful application of the symmetric property of equality is that reorganizing equations makes it easier to solve systems of equations. For example, if one had two linear equations, 11 = 2x + 5 and -2x + 3y = 6, the symmetric property of equality allows the equations to be ordered so that they can be added together. Thanks to the symmetric property of equality, 11 = 2x + 5 can be transformed to say 2x + 5 = 11. One can add the two equations together to solve for y: (-2x + 3y = 6) + (2x + 5 = 11). These two equations sum to 3y + 5 = 17.

This simplifies to 3y = 12, or y = 4. Then by substituting in for y, -2x + 3(4) = 6; this yields -2x + 12 = 6, or -2x = -6, or x = 3. So the solution to the linear system is x = 3, y = 4.

Learn more about Arithmetic-
Q:
## What is an example of distributive property of multiplication over addition?

A: An example of the how the distributive property distributes multiplication over an addition problem is: x(y + z) = (xy + xz). In other words, "x" is multip... Full Answer >Filed Under: -
Q:
## What is the commutative property of addition?

A: The commutative property of addition states that numbers or terms being added together can be rearranged without changing the final result. For example, 2 ... Full Answer >Filed Under: -
Q:
## What does distributive property mean?

A: The distributive property is a mathematical and algebraic property that says that multiplying two numbers is the same as multiplying one of those numbers b... Full Answer >Filed Under: -
Q:
## What is the associative property of multiplication?

A: The associative property of multiplication states that the order in which numbers are multiplied in sequence is irrelevant. In other words, if more than tw... Full Answer >Filed Under: