Question

Which describes the system of equations below?

y
=
–5
3
x
−
4
9

y
=
–5
3
x
+
9
2

Answer 1

To analyze the system of equations given, let's rewrite them clearly:

1. \( y = -\frac{5}{3}x - \frac{4}{9} \)
2. \( y = -\frac{5}{3}x + \frac{9}{2} \)

Let's examine the characteristics of these equations:

1. **Slope**: Both equations have the same slope, which is \( -\frac{5}{3} \). This means the lines are parallel.

2. **Y-Intercept**:
- The first equation has a y-intercept of \( -\frac{4}{9} \).
- The second equation has a y-intercept of \( \frac{9}{2} \).

Since the lines are parallel and have different y-intercepts, they will never intersect.

### Conclusion:
This system of equations has no solution, as it consists of two parallel lines.