To solve the system of equations, we can use the method of substitution or elimination.

Let's start by solving the first equation for x:

2x + y = 5
y = 5 - 2x

Now substitute this value of y into the second equation:

7x + 8(5-2x) = 22
7x + 40 - 16x = 22
-9x + 40 = 22
-9x = -18
x = 2

Now that we have found the value of x, we can substitute it back into the first equation to find y:

2(2) + y = 5
4 + y = 5
y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.