Question

Which pair of linear equations has a graph that has exactly one solution?
A.
(a =- 2y
1
①9= =2¢+5
В.
9=2+3
19=20+1
C. <
1y = 2x - 3
(y = 7x - 1
D.
[y= ⅓ㄻ

Answer 1

To determine which pair of linear equations has a graph that has exactly one solution, we need to analyze each option for their slopes and y-intercepts. Two linear equations have exactly one solution if they intersect at exactly one point, which occurs when their slopes are different (i.e., they are not parallel).

Let's analyze the options:

### A.
1. \( y = -2x + 1 \) (rearranged from \( a = -2y \))
2. \( y = 2x + 5 \)

- Slopes:
- First equation slope = -2
- Second equation slope = 2
- Since the slopes are different, these lines intersect at exactly one point.

### B.
1. \( y = 2x + 3 \)
2. \( y = 2x + 1 \)

- Slopes:
- Both equations have a slope of 2.
- Since the slopes are the same, these lines are parallel and have no solutions.

### C.
1. \( y = 2x - 3 \)
2. \( y = 7x - 1 \)

- Slopes:
- First equation slope = 2
- Second equation slope = 7
- Since the slopes are different, these lines intersect at exactly one point.

### D.
- You didn't provide the second equation. It seems to be incomplete so we cannot analyze it.

### Conclusion:
Options **A** and **C** both have graphs that intersect at exactly one point. Therefore, the pairs of linear equations that have exactly one solution are options **A** and **C**.