To determine how many solutions the system of equations has, let’s take a closer look at the equations given:
Equation 1: y = 3.5x + 3.5
Equation 2: y = 3.5x + 3.5
Both equations are identical. When you have two equations that are exactly the same, they represent the same line on a graph.
In this case, since both equations describe the same line, they will intersect at every point along that line. This means that there are infinitely many solutions to this system of equations because any point (x,y) that lies on the line described by y = 3.5x + 3.5 is a valid solution.
To visualize this, imagine drawing the line represented by the equation on a Cartesian plane. Every coordinate pair (x, y) that satisfies this equation is a solution.
In conclusion, this system has infinitely many solutions because the two equations are the same, meaning they overlap completely.