Here are the answers to your questions:
1. **Which of the following points, if any, are solutions to the system of equations?**
- To see if the points (0, 2) or (0, -4) are solutions to the system of equations \(y = 2x + 2\) or \(y = 2x - 4\):
- For (0, 2):
- In the first equation \(y = 2x + 2\): \(2 = 2(0) + 2 \rightarrow 2 = 2\) (True)
- In the second equation \(y = 2x - 4\): \(2 = 2(0) - 4 \rightarrow 2 = -4\) (False)
- For (0, -4):
- In the first equation \(y = 2x + 2\): \(-4 = 2(0) + 2 \rightarrow -4 = 2\) (False)
- In the second equation \(y = 2x - 4\): \(-4 = 2(0) - 4 \rightarrow -4 = -4\) (True)
- **Correct Response:** Neither of these points are solutions.
2. **Which of the following points can be used to best estimate the time when the divers are at the same depth?**
- To find the point where the divers are at the same depth, you would look for points where both lines intersect. If the graphs, not provided here, show which points are best approximations of the intersection, then:
- Assuming we look for equality in depth (y-values), the best option among the provided choices has to be closest to the point of intersection.
- **Without the graph, I can't give a definitive answer**, but analyze each choice based on proximity to the intersection point.
3. **What is the best approximate solution to the system of equations graphed?**
- **Without the graph**, I can't identify the exact intersection point, but it would generally be the point where the two lines cross, given in the choices.
- Look for the point that visually appears to intersect both lines.
4. **Which statement best describes the system of equations {y=−3x+7, y=−3x−7}?**
- Both equations have the same slope of -3, but different y-intercepts (7 and -7).
- **Correct Response:** Both equations have a slope of −3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.
5. **Which of the following systems of linear equations has no solution?**
- Systems of equations have no solution when the equations are parallel (same slopes, different y-intercepts):
- System A: {4x + y = 17, 4x - y = 3} (Different slopes)
- System B: {4x - y = -17, 4x + y = 3} (Different slopes)
- System C: {4x - y = 17, 4x + y = 3} (Different slopes)
- System D: {4x - y = 17, 4x - y = 3} (Same slopes, same y-intercept, thus infinitely many solutions)
- **Correct Response:** {4x - y = 17, 4x + y = 3} or {4x + y = 17, 4x - y = 3}, depending on specific slopes.
Would you like any further clarifications or a deeper explanation?