Solve the system of equations by graphing.
\[
\begin{array}{l}
x+y=7 \\
2 x+2 y=14
\end{array}
\]
Use the graphing tool to graph the system.
Determine the solution of the system of equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is $\square$. (Type an ordered pair.)
B. There are infinitely many solutions.
c. There is no solution.
Answer
\(\boxed{\text{Therefore, there are infinitely many solutions to this system of equations, as every point on the line } x + y = 7 \text{ is a solution.}}\)
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 ：\(\boxed{\text{Therefore, there are infinitely many solutions to this system of equations, as every point on the line } x + y = 7 \text{ is a solution.}}\)
