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Solve for x and y Y=2x-7 and x²-2x+y²-2y=70​

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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.

User Abhimanyu Daspan
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