Question

or
Graph these equations:
y=
1
2
x–7
y=
1
2
x–2
Click to select points on the graph.
How many solutions does the system of equations have?

Answer 1

Let's analyze the equations you've provided:

1. \( y = \frac{1}{2}x - 7 \)
2. \( y = \frac{1}{2}x - 2 \)

Both equations are linear equations with the same slope of \( \frac{1}{2} \). This means they are parallel lines.

### Graphing the Equations:
- The first equation has a y-intercept of \(-7\), which means it crosses the y-axis at the point \( (0, -7) \).
- The second equation has a y-intercept of \(-2\), which means it crosses the y-axis at the point \( (0, -2) \).

### Solution Analysis:
Parallel lines never intersect, which implies that there is no point at which both equations are satisfied simultaneously. Therefore, the system of equations has **no solutions**.

In summary, the number of solutions to the system of equations is **0**.