Q:

# What is the symmetric property of equality?

A:

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.

## Keep Learning

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.

Sources:

## Related Questions

• A: There are five major properties of addition in math: the commutative property, the associative property, the distributive property, the identity property a... Full Answer >
Filed Under:
• A: Teach children with a 1 to 100 times table chart by using strategies such as skip counting, the commutative property for multiplication and looking for pat... Full Answer >
Filed Under:
• 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:
• A: To perform partial product multiplication, you use the distributive property of numbers, multiplying each digit of a number by each digit of the other numb... Full Answer >
Filed Under:
PEOPLE SEARCH FOR