Here are the original equations:
2x + 2y = 14
x + 2y = 11
We immediately note that these two equations form a system. So, we can use substitution to solve the second equation for x. To do this, all that needs to be done is to subtract 2y from both sides, to get x = 11 - 2y. Next, we substitute the derived expression for x into the first equation to get 2(11-2y) + 2y = 14. We can use the distribute property to get 22 - 4y + 2y = 14. Then, we can combine like terms to get 22 - 2y = 14. After that, we subtract 22 from both sides to get -2y = -8. Finally, we divide -2 from both sides to get y = 4.
Now that we have the value for y, we can substitute our derived value into the second equation, since it will be much faster. After doing this, we get x + 2(4) = 11. We can simplify the left side of the equation and subtract the product from both sides, which gives us x = 4. Therefore, the answer to your query is x = 4, y = 4. Hope this helps and happy Halloween!
