5x=10y is an algebraic equation that represents a relationship between two variables, x and y. Let’s break it down and understand its meaning and implications:

  1. Equation breakdown:
    • 5x = 10y
    • The equation states that if you multiply a number (x) by 5, it will be equal to multiplying another number (y) by 10.
    • In simpler terms, it means that the value of 5 times x is equal to the value of 10 times y.
  2. Solving for y:
    • To solve for y, we can rearrange the equation.
    • Divide both sides of the equation by 10: (5x)/10 = y.
    • Simplifying further, we have y = x/2.
    • This tells us that the value of y is half of the value of x.
  3. Examples:
    • Let’s consider a few examples to illustrate this equation:
      • If x = 2, then y = 2/2 = 1.
      • If x = 10, then y = 10/2 = 5.
      • If x = -6, then y = -6/2 = -3.
  4. Understanding the relationship:
    • The equation 5x=10y represents a linear relationship between x and y.
    • For every value of x, we can find a corresponding value of y that satisfies the equation.
    • As x increases, y will also increase, but at half the rate.
    • Similarly, as x decreases, y will decrease, but at half the rate.
    • The two variables, x and y, are proportional, with a constant ratio of 5:10 or 1:2.

In conclusion, the equation 5x=10y demonstrates a proportional relationship between x and y, where y is always half of x. By understanding this equation, you can solve for one variable given the other and interpret the relationship between the two variables.

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