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Which of the following statements is true about the linear equation 4x - 5y = 20

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Question: Which of the following statements is true about the linear equation 4x - 5y = 20?

Options:

  1. It has no solutions.
  2. It has infinitely many solutions.
  3. It has exactly one solution.
  4. It is a quadratic equation.

Correct Answer: It has exactly one solution.

Solution: 

A linear equation in two variables has exactly one solution unless it is a special case (like parallel lines). Here, it is a standard linear equation.

Which of the following statements is true about the linear equation 4x - 5y = 20

Practice Questions

Q1
Which of the following statements is true about the linear equation 4x - 5y = 20?
  1. It has no solutions.
  2. It has infinitely many solutions.
  3. It has exactly one solution.
  4. It is a quadratic equation.

Questions & Step-by-Step Solutions

Which of the following statements is true about the linear equation 4x - 5y = 20?
  • Step 1: Understand what a linear equation is. A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants.
  • Step 2: Identify the given equation. The equation we have is 4x - 5y = 20.
  • Step 3: Recognize the form of the equation. The equation 4x - 5y = 20 is in the standard form of a linear equation.
  • Step 4: Determine the number of solutions. A standard linear equation in two variables typically has one solution unless it represents parallel lines (which have no solutions) or the same line (which has infinitely many solutions).
  • Step 5: Conclude that since 4x - 5y = 20 is a standard linear equation, it has exactly one solution.
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