Sure, I'd be happy to help you solve this system of equations!
First, let's solve the first equation for x:
x = 2y - 7
Now, substitute this expression for x into the second equation:
(2y - 7)² - 2(2y - 7) + y² - 2y = 70
Expand and simplify:
4y² - 14y + 7 - 2y + 7 = 70
Combine like terms:
4y² - 12y + 7 = 70
Now, let's factor the left-hand side:
(2y - 3)(2y - 2) = 70
We can see that (2y - 3) and (2y - 2) are both factors of 70, so we can write:
2y - 3 = 10 or 2y - 2 = 15
Solving for y in the first equation:
y = 3/2 or y = 2/3
Now, substituting these expressions for y into the first equation, we get:
x = 2(3/2) - 7 = 6/2 - 7 = -1/2
x = 2(2/3) - 7 = 4/3 - 7 = -3/3
So, the solutions to the system are x = -1/2 and y = 3/2, and x = -3/3 and y = 2/3.
I hope this helps! Let me know if you have any other questions.