To solve the system of equations, we start by writing down the two equations:
- x + 2y = 7
- x + 2y = 1
If we look closely at these two equations, we can see that they both have the same left-hand side: x + 2y. This means that both equations are representing the same expression on the left but equating it to different values on the right.
Now, if we set the right-hand sides equal to each other, we have:
7 = 1
This statement is clearly false, indicating that there are no values for x and y that can satisfy both equations simultaneously. Hence, the system of equations is inconsistent.
In conclusion, the solution to the system of equations x + 2y = 7 and x + 2y = 1 is that there is no solution.