Question

Graph these equations:
y=3x+4
y=3x–1
Click to select points on the graph.
How many solutions does the system of equations have?

Answer 1

To graph the equations \( y = 3x + 4 \) and \( y = 3x - 1 \):

1. **Graph the first equation, \( y = 3x + 4 \)**:
- This is a linear equation with a slope of 3 and a y-intercept of 4.
- To plot it, you can start at the y-intercept (0, 4) and use the slope to find another point. From (0, 4), you can move up 3 units and right 1 unit to get to (1, 7).

2. **Graph the second equation, \( y = 3x - 1 \)**:
- This is also a linear equation with a slope of 3 and a y-intercept of -1.
- Start at the y-intercept (0, -1). Using the slope of 3, move up 3 units and right 1 unit to get to (1, 2).

3. **Observe the lines**:
- Both lines have the same slope (3), which means they are parallel.
- Since the y-intercepts (4 and -1) are different, the lines will never intersect.

**Conclusion**:
The system of equations has **no solutions** because the two lines are parallel and do not intersect.