To determine which graph represents the system of equations with no solution, we first need to analyze the equations provided:
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\( y = 2x + 4 \)
- This is a linear equation with a slope of 2 and a y-intercept at (0, 4).
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\( -2x + y = 8 \)
- Rearranging this gives us \( y = 2x + 8 \).
- This line also has a slope of 2, but a different y-intercept at (0, 8).
Since both lines have the same slope (2) but different y-intercepts (4 for the first line and 8 for the second), they are parallel lines. Parallel lines never intersect, which means the system of equations has no solution.
Now we need to look for the graph where the solid line represents \( y = 2x + 4 \) (passing through (0, 4) and (−2, 0)), and the dashed line corresponds to \( y = 2x + 8 \) (passing through (0, 8) and another point that maintains parallelism).
From your descriptions:
- The graph on the first option shows the solid line passing through (0, 4) and another point that implies it has the same slope as the dashed line, passing through (0, 8). Thus, this graph shows parallel lines.
Based on the equations and the information given, the correct graph representing the system of equations with no solution is the first one:
A coordinate plane with 4 quadrants... The solid line passes through (0, 4) and (−2, 0). The dashed line passes through (−4, 0) and (0, 8).