y = 5x – 1

Question

–15x – 3y = 3
How many solutions does this linear system have?

one solution: (0, –1)
one solution: (1, 4)
no solution
infinite number of solutions

Answer 1

To determine how many solutions the given linear system has, we can analyze the equations provided.

1. The first equation is: \[ y = 5x - 1 \]

2. The second equation is: \[ -15x - 3y = 3 \] We can rearrange this into slope-intercept form (y = mx + b) to see if it represents the same line. First, solve for \( y \): \[ -3y = 15x + 3 \] \[ y = -5x - 1 \]

Now we have two equations:

1. \( y = 5x - 1 \)
2. \( y = -5x - 1 \)

Next, we observe that the slopes of these equations (5 and -5) are different. This indicates that the two lines are not parallel and will eventually intersect. Since the lines intersect at one point, this system of equations has one solution.

So, the conclusion is: one solution.