Question

Which of the following is an equation with one constant, two coefficients, and three terms? (1 point)
• 3х - у = 5у
• 3х - 4у = 5х
• 3x - 4у = 5у
• 3х - 4 = 5у

Answer 1

To determine which of the given options represents an equation with one constant, two coefficients, and three terms, let’s analyze each option.

1. **3x - y = 5y**
- Rearranging gives: 3x - y - 5y = 0 → 3x - 6y = 0
- Terms: 3x, -6y, and 0 (a constant)

2. **3x - 4y = 5x**
- Rearranging gives: 3x - 5x - 4y = 0 → -2x - 4y = 0
- Terms: -2x, -4y, and 0 (a constant)

3. **3x - 4y = 5y**
- Rearranging gives: 3x - 4y - 5y = 0 → 3x - 9y = 0
- Terms: 3x, -9y, and 0 (a constant)

4. **3x - 4 = 5y**
- Rearranging gives: 3x - 5y - 4 = 0
- Terms: 3x, -5y, and -4 (a constant)

Now, let's look for the one that has exactly **one constant**, **two coefficients**, and **three terms**.

Upon analysis:
- All of the equations have two coefficients (for x and y) and one constant term.
- Each equation has three terms when written in the form of \(Ax + By + C = 0\) or rearranging.

Every option fits the criterion; however, the most clear vector for the one constant included in the equation itself is:

**Option 4: 3x - 4 = 5y**

This equation shows the constant (-4) explicitly, thus clearly identifying itself in that context.

Final Conclusion:
The equation with one constant, two coefficients, and three terms is: **3x - 4 = 5y**.