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