In order to determine which system would have only one solution, we need to understand how lines relate to each other in terms of intersections.
- Lines a and b intersect - This means they are not parallel and will cross at one point, which gives us one solution.
- Lines c and d are the same line - If two lines are the same, they do not intersect at a unique point but instead are coincident, which means they have infinitely many solutions (every point on the line is a solution).
Let's analyze the options:
A. Line a and line b - These two lines intersect at one point, so they have one solution.
B. Line b and line c - Line b is distinct and intersects line c (which is the same line as line d), hence they will also have infinitely many solutions as line c and d do not intersect uniquely.
C. Line b and line d - Similar to line b and line c, line d is the same as line c, leading to infinitely many solutions (they are the same line).
D. Line c and line d - Since these lines are the same, they also have infinitely many solutions.
From this analysis, the only pair that results in a unique solution (one intersection point) is:
A. Line a and line b.
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