How Many Solutions Does the Linear System y = 5x + 1 and 15x + 3y = 3 Have?

To determine how many solutions the linear system has, we need to analyze the two equations:

• Equation 1: y = 5x + 1
• Equation 2: 15x + 3y = 3

First, let’s rearrange the second equation to the slope-intercept form (y = mx + b). We can start by isolating y:

15x + 3y = 3
3y = -15x + 3
y = -5x + 1

Now we have two equations:

1. y = 5x + 1
2. y = -5x + 1

If we plot these two lines, we see that they have different slopes (5 and -5) and the same y-intercept (1). This means the lines will intersect at exactly one point.

Thus, the linear system has one solution.