Which statement about this equation is true?

3y–1=13–4y

Responses

The equation has no solution.
The equation has no solution.

The equation has one solution.
The equation has one solution.

The equation has a few solutions.
The equation has a few solutions.

The equation has many solutions.

1 answer

To determine the truth about the equation \(3y - 1 = 13 - 4y\), we can solve it step by step.

  1. Start with the original equation: \[ 3y - 1 = 13 - 4y \]

  2. Add \(4y\) to both sides: \[ 3y + 4y - 1 = 13 \] \[ 7y - 1 = 13 \]

  3. Add \(1\) to both sides: \[ 7y = 13 + 1 \] \[ 7y = 14 \]

  4. Now, divide both sides by \(7\): \[ y = \frac{14}{7} = 2 \]

Since we found a single value \(y = 2\) that satisfies the equation, we can conclude that the equation has one solution.

Thus, the correct statement is: The equation has one solution.