Write the equation x = 2y in the form ax + by + c = 0, and find out the values of a, b, and c.

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Points to Remember:

  • The equation needs to be rearranged into the standard form of a linear equation: ax + by + c = 0.
  • We need to identify the values of a, b, and c after the rearrangement.

Introduction:

The given equation, x = 2y, represents a linear relationship between two variables, x and y. It can be graphically represented as a straight line. Linear equations are fundamental in algebra and have numerous applications in various fields, from physics and engineering to economics and finance. The standard form, ax + by + c = 0, allows for easy comparison and manipulation of linear equations.

Body:

Rearranging the Equation:

To express the equation x = 2y in the form ax + by + c = 0, we need to manipulate the terms:

  1. Subtract x from both sides: 0 = 2y – x
  2. Rearrange the terms: -x + 2y + 0 = 0

Now the equation is in the desired form: ax + by + c = 0.

Identifying the Values of a, b, and c:

By comparing our rearranged equation (-x + 2y + 0 = 0) with the standard form (ax + by + c = 0), we can identify the values of a, b, and c:

  • a = -1 (the coefficient of x)
  • b = 2 (the coefficient of y)
  • c = 0 (the constant term)

Conclusion:

In conclusion, the equation x = 2y can be written in the standard form ax + by + c = 0 as -x + 2y + 0 = 0. Therefore, the values are a = -1, b = 2, and c = 0. This simple transformation demonstrates a fundamental algebraic manipulation, highlighting the importance of understanding different forms of linear equations and their inter-convertibility. This understanding is crucial for further mathematical operations and applications in various fields, emphasizing the importance of foundational algebraic skills.

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