Same y terms but opposite signs

Same y terms but Opposite Signs

Concept Understanding

• This refers to the scenario where a mathematical equation or a set of equations have variables (often ‘y’) with exactly equal numerical values but different signs, which could be positive or negative.

• The importance of this concept lies in its application in algebraic manipulation, particularly for simplifying expressions and solving equations.

Application Steps

• First, identify the like terms (same variable and power, different signs) in the equation or expression.

• When like terms with opposite signs are combined, they cancel each other out, that is, they sum up to zero.

• If it’s an equation, after cancelling out the like terms with opposite signs, you’ll be left with a simplified form of the equation that you can solve more easily.

Examples

• Consider the equation: 3y - 2 + y - y + 4 = 8. In this case, ‘y’ and ‘-y’ are like terms with opposite signs. They cancel out each other, simplifying the equation to 3y - 2 + 4 = 8.

• In the algebraic expression 4y - 2y + 9 - y + y, ‘y’ and ‘-y’ are like terms with opposite signs. They cancel out, simplifying the expression to 4y - 2y + 9.

In Summary

• Identifying and handling like terms with opposite signs is a key part of algebraic manipulations that simplifies expressions and equations.

• Regular practice with problems involving like terms with different signs is recommended to get comfortable with this concept.

• Always remember: The sum of a number and its opposite is always zero!