Solve the following system of equations. How many solutions are there? x + y = 2 5x + 5y = 10 a) There is no solution. b) There are infinite solutions. c) There is one solution.

we are given the following system of equations:[tex]\begin{gathered} x+y=2,\text{ (1)} \\ 5x+5y=10,\text{ (2)} \end{gathered}[/tex]Equation (2) can be rewritten dividing by 5 on both sides as:[tex]\frac{5x}{5}+\frac{5y}{5}=\frac{10}{5}[/tex]Solving the operations:[tex]x+y=2,\text{ (2)}[/tex]Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.