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:
- \( y = 3x + 6 \)
- \( y = -13x - 4 \)
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.