2. Consider this system of linear equations: $\left\{\begin{array}{l}y=\frac{4}{5} x-3 \\ y=\frac{4}{5} x+1\end{array}\right.$ a. Without graphing determine how many solutions you would expect this system of equations to have. Explain your reasoning b. Try solving the system of equations algebraically and describe the result tha you get. Does it match your prediction?

Step 1 ：The system of equations given are both in the form of y = mx + c, where m is the slope and c is the y-intercept. If two lines have the same slope (m), they are either the same line (if they also have the same y-intercept) or parallel lines (if they have different y-intercepts). In this case, both lines have the same slope (4/5), but different y-intercepts (-3 and 1). Therefore, they are parallel lines. Parallel lines never intersect, so there should be no solutions to this system of equations.

Step 2 ：To confirm this, we can try to solve the system of equations algebraically. Since both equations are already solved for y, we can set them equal to each other and solve for x. If we get a valid value for x, we can substitute it into either equation to get a corresponding value for y. If we get an invalid value (like a contradiction), it confirms that there are no solutions.

Step 3 ：The solution returned an empty list, which means there are no solutions to the system of equations. This matches our initial prediction that there would be no solutions because the lines are parallel.

Step 4 ：Final Answer: The system of equations has \(\boxed{0}\) solutions.