To solve the system of equations given by x + 2y = 7 and x + 2y = 1, we need to analyze the equations more closely.
First, we can observe that both equations have the same left-hand side, x + 2y. This means they represent two different situations for the same expression:
- From the first equation: x + 2y = 7
- From the second equation: x + 2y = 1
Setting the left-hand sides equal to each other gives us:
x + 2y = 7
x + 2y = 1
Thus, we can equate them:
7 = 1
This statement is clearly false, indicating that there is no possible solution where both equations can be true simultaneously.
Therefore, we conclude that the system of equations is inconsistent. The lack of a common solution means that there are no values of x and y that satisfy both equations at the same time.
In conclusion, the system of equations x + 2y = 7 and x + 2y = 1 does not have a solution.