Question

is this no solution, infinite solutions, or one solution. y = 3x + 6, y = -13x - 4

Answer 1

To determine whether the system of equations has no solution, infinite solutions, or one solution, we can analyze the slopes and intercepts of the lines represented by the equations.

The equations given are:
1. \( y = 3x + 6 \)
2. \( y = -13x - 4 \)

### Step 1: Identify the slopes

From the first equation, \( y = 3x + 6 \), the slope (m) is \( 3 \).

From the second equation, \( y = -13x - 4 \), the slope (m) is \( -13 \).

### Step 2: Compare the slopes

Because the slopes \( 3 \) and \( -13 \) are different, the two lines intersect at exactly one point.

### Conclusion

This means the system of equations has **one solution**.