Question
If the four lines are extended, which system would have only one solution?
On a coordinate plane, lines a and b would intersect. Lines c and d are the same line.
A. line a and line b
B. line b and line c
C. line b and line d
D. line c and line d
On a coordinate plane, lines a and b would intersect. Lines c and d are the same line.
A. line a and line b
B. line b and line c
C. line b and line d
D. line c and line d
Answers
GPT-4o mini
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.
1. **Lines a and b intersect** - This means they are not parallel and will cross at one point, which gives us one solution.
2. **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**.
1. **Lines a and b intersect** - This means they are not parallel and will cross at one point, which gives us one solution.
2. **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**.