Question

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.

Answer 1

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.**