To determine the correct system of equations based on the information provided in the question, we need to establish the equations of the lines based on the given points and the characteristics of the slopes.
- The solid line passes through the point (2, 7).
- The dotted line intersects the first line at the point (-1, 1).
From the information, we can infer:
- For the first line (solid line), we can denote its equation in slope-intercept form as \( y = mx + b \).
- The second line intersects the first line at (-1,1), which gives us another point we can use to find its equation.
Let's analyze the possible equations given in the responses:
-
{y=2x+3, y=3x+4}
- The first line \( y = 2x + 3 \) does not pass through (2, 7) since substituting x=2 gives us y=7, but we need y=7 to equal 7, which works. However, the second line doesn't fit either as it won't intersect at (-1, 1).
-
{y=2x−3, y=3x−4}
- The first line \( y = 2x - 3 \) does not have the point (2, 7) since substituting x=2 gives us 2(2) - 3 = 1, which isn't correct. The second line won't fit either since it doesn't intersect at (-1,1).
-
{y=3x+2, y=4x+3}
- The first line \( y = 3x + 2 \) at (2,7) yields \( y = 3(2) + 2 = 8 \), wrong point and similarly won't pass through (-1, 1).
-
{y=−x+1, y=2x+7}
- The first line \( y = -x + 1 \) evaluated at (-1) gives \( 1 + 1 = 2\), passing through (-1,1) checking would make sense while the second line obviously doesn't intersect through (2,7).
We need further verification that meets both criteria. Since subjective analysis couldn't yield concrete answers confirming all distinct intersection points, Based on point conclusion neither provided matched the criteria distinctly...
Thus, none of them seem to match the criteria accurately. However, please check for other matching endpoints and correction, or visual data for conforming, if available.