Question

A system of equations is graphed on the coordinate plane.

y=12x+4y=12x+3



Select the number of solutions for the system of equations from the drop-down menu.


Choose...

Graph of the equation y equals point five x plus three and the equation y equals point five x plus four.

Answer 1

To determine the number of solutions for the given system of equations, we first need to analyze the equations provided.

1. **The equations given:**
- \( y = 12x + 4 \)
- \( y = 12x + 3 \)

Since both equations are in the form \( y = mx + b \), we can see that they have the same slope \( (m = 12) \) but different y-intercepts (\( b = 4 \) for the first equation and \( b = 3 \) for the second equation).

2. **Interpreting the graph:**
- Since the slopes are the same and the y-intercepts are different, the two lines are parallel. Parallel lines do not intersect at any point on the coordinate plane.

3. **Conclusion:**
- Therefore, the system of equations has no solutions.

For the second mention of equations:
- **Assuming the equations are:**
- \( y = 0.5x + 3 \)
- \( y = 0.5x + 4 \)

Similar to the first equations, these lines also have the same slope \( (m = 0.5) \) but different y-intercepts (\( b = 3 \) and \( b = 4 \)).

This also means that:

- The second pair of equations are also parallel and do not intersect.

Thus, this system also has no solutions.

**In summary**, for both cases, the number of solutions for both systems of equations is:
- **No solutions.**