To find the solution set of the given system of equations, we need to solve them simultaneously.
The first equation is:
5x + 2y = 7
The second equation is:
y = x + 1
We can substitute the expression for y from the second equation into the first equation:
5x + 2(x + 1) = 7
Now, simplify this equation:
5x + 2x + 2 = 7
This simplifies to:
7x + 2 = 7
Subtract 2 from both sides:
7x = 5
Now, divide by 7:
x = 5/7
Now that we have the value of x, we can substitute it back into the second equation to find y:
y = (5/7) + 1
Convert 1 to a fraction:
y = (5/7) + (7/7) = (12/7)
So, the solution set of the system of equations is:
(x, y) = (5/7, 12/7)
In conclusion, the solution set to the system of equations is (5/7, 12/7).