Step 1 :The given system of equations is: \(x + y = 7\) and \(2x + 2y = 14\)
Step 2 :We can simplify the second equation by dividing each term by 2: \(\frac{2x}{2} + \frac{2y}{2} = \frac{14}{2}\)
Step 3 :This simplifies to: \(x + y = 7\)
Step 4 :Now, we can see that the two equations are identical. This means that they represent the same line on a graph.
Step 5 :\(\boxed{\text{Therefore, there are infinitely many solutions to this system of equations, as every point on the line } x + y = 7 \text{ is a solution.}}\)