3(x+y)+1=x+4y
Expanding the left side, we get:
3x + 3y + 1 = x + 4y

Subtracting x from both sides:
2x + 3y + 1 = 4y

Subtracting 3y from both sides:
2x + 1 = y

Now, let's solve the second equation:

7 - 2(x-y) = x - 8y
Expanding the left side, we get:
7 - 2x + 2y = x - 8y

Adding 2x to both sides:
7 + 2y = 3x - 8y

Adding 8y to both sides:
7 + 10y = 3x

Dividing by 3 on both sides:
(7 + 10y) / 3 = x

Now, we have the two equations:
2x + 1 = y
(7 + 10y) / 3 = x

We can substitute the value of x from the second equation into the first equation to solve for y:
2(7 + 10y) / 3 + 1 = y
14 + 20y / 3 + 1 = y
14 + 20y / 3 - 3y / 3 = y
14 + 17y / 3 = y
y = 14 / 3

Now we can substitute the value of y back into the second equation to solve for x:
x = (7 + 10(14 / 3)) / 3
x = (7 + 140 / 3) / 3
x = (21 + 140) / 3
x = 161 / 3

Therefore, the solution to the system of equations is:
x = 161 / 3
y = 14 / 3