Use the image to answer the question.

To determine the system of equations represented by the given graph, we can focus on the clues provided regarding the two lines and their respective points:

1. **Solid Line through (2, 7):** This point is on the solid line, and we can use it to determine the equation of this line. Since it slopes upward and passes through (2, 7), we can write it generally in the slope-intercept form \( y = mx + b \). The exact slope can be determined by analyzing the graph, but typically we can assume a slope of 2 or another reasonable positive slope when the exact values of other points on the line are not given.

2. **Dotted Line intersects at (-1, 1):** This point lies on the dotted line, intersecting the solid line at the specified coordinate.

Given the available response options and the mentioned points, let's examine them one by one.

- **Option 1:** {y=2x+3, y=3x+4}
- If we substitute x=2 in \( y=2x+3 \): \( y=2(2)+3 = 7 \) which is valid, but not corroborated by the other line through (-1, 1).

- **Option 2:** {y=3x+2, y=4x+3}
- Substituting x=2 in \( y=3x+2 \): \( y = 3(2) + 2 = 8 \) which doesn't fit with the known point.

- **Option 3:** {y=−x+1, y=2x+7}
- Substituting x=2 in \( y=2x+7 \): \( y=2(2)+7 = 11 \), which is not valid with the existing point at (2, 7).

- **Option 4:** {y=2x−3, y=3x−4}
- Substituting x=2 in \( y=2x-3 \): \( y=2(2)-3 = 1 \), which is not valid with the known point (2, 7).

Reviewing each response in light of the points mentioned (the positions of (2, 7) and (-1, 1)) will clarify things further.

The final best fitting response from the options is:

- The **system of equations** that includes the point (2, 7) for one line and logically intersects with the other line at (-1, 1) after proper substitution into the equations.

Based on logic rather than direct equations and deducing from the graph, we would attempt to confirm through interaction of coordinates which best fit.

However, considering typical slopes of intersecting lines and the graphical representation, if exact numerical calculations do not contradict apparent visual assessment, options may need to be approached conceptually for visual approximation.

Therefore the sought representation may be an error from oversight in exchanging negative reciprocal or mixed slope design, cautious speaking would derive accurate representations if visual graphs were hand-tailored to match specific equations through graphical checking upon each stated point until concrete relations formed.

With assumptions made from correlating properties of lines (positive and negative slopes visually established), the equations can draw closer relations for final determinations although if visual completion mismatches plotted values.