Same y terms but both signs are negative

Same y Terms but Both Signs are Negative

Understanding the Basics

  • Algebraic equations are mathematical expressions involving variables and constants interconnected by algebraic operations such as addition, subtraction, multiplication, and division.

  • In a situation where two identical y terms have a negative sign, the aim is to simplify the equation to determine the unknown variable.

Key Characteristics

  • The primary characteristic of an equation with ‘same y terms but both signs are negative’ is the presence of y terms with an identical absolute value but with a negative sign.

  • For instance, the equation -5y - 3 = -5y + 2 showcases two identical y terms with different signs.

Pointers for Solving these Equations

  1. While working with an equation exhibiting negative y terms, the ultimate goal is to isolate y to derive its value.

  2. As a first step, cancel out the y terms that appear on both sides of the equation.

  3. Following the elimination of y, simplify the constants through an appropriate algebraic operation which will render the solution for the variable y.

Example Demonstrations

  • In the equation -5y - 3 = -5y + 2, if the y terms are eliminated from both sides, this leaves -3 ≠ 2. This indicates that the initial equation is not possible as -3 and 2 are not equal values.

  • For another example, in the equation -2y - 4 = -2y + 7, cancelling the y terms leaves -4 ≠ 7, further denoting a contradictory equation.

In Conclusion

  • Whenever, you observe a scenario with ‘same y terms but both signs are negative’, aim to eliminate matching y terms and simplify the remaining constants.

  • It’s important to note that such equations usually lead to a contradiction, indicating that they have no possible solution.

  • Irrespective of this, it is crucial to understand and be proficient in manipulating these types of equations, as they form a part of the wider algebraic landscape.