Linear Equations

• An equation is a mathematical statement that tells you that two quantities are equal in value.
• To determine whether a mathematical statement is an equation, look for the equal sign (=). If there’s a presence of an equal sign, then the mathematical statement is an equation.
• The properties of equality are rules or principles that allow us to manipulate equations to determine the values of the unknown variable. 
• Reflexive Property of Equality

  This property is pretty evident and logical. The value of a number is always equal to itself.  For instance, 1020 will always be equal to 1020. If someone tells you that 1020 = 1100, he is logically false since 1020 is always equal to 1020 by the reflexive property.
• Symmetric Property of Equality

  This property tells us that if we switch the positions of the quantities on the left-hand side and the right-hand side of the equation, the equation will still hold. This also implies that both sides of the equation are of the same value.
• Transitive Property of Equality

  The transitive property of equality tells us that if a quantity is equal to a second quantity, and if the second quantity is equal to a third quantity, then we can conclude that the first quantity is equal to the third quantity.
• Addition Property of Equality (APE)

  APE tells us that the result will still be equal if we add a specific number to two equal quantities. 
• Subtraction Property of Equality (SPE)

  The equality will remain if we subtract a number from two equal quantities.
• Formally, linear equations in two variables are in ax + by = c form, where a, b, and c are real numbers and a and b are nonzero.