To determine how many solutions the system of equations y = 3.5x and y = 3.5x has, we need to analyze the equations carefully.
First, let’s rewrite the equations for clarity:
- Equation 1: y = 3.5x
- Equation 2: y = 3.5x
Now, you might notice that both equations are exactly the same. This means that they represent the same line on a coordinate plane. When two equations define the same line, every point on this line is a solution to the system of equations.
In other words, since both equations are identical, there are infinitely many solutions because any point (x, y) that lies on the line described by y = 3.5x is a solution. If you pick any value for x, you can find a corresponding y value using the equation.
Moreover, if we graph the equations, they overlap entirely as they are the same line. Therefore, it confirms that:
- There are infinitely many solutions to the system of equations.
In summary, because both equations are the same, the answer is that there are infinitely many solutions to the system of equations defined by y = 3.5x and y = 3.5x.