Answer:
Starting with the given system of equations:
2 - x = 5y
y^2 + x = xy + y
We can rearrange the first equation to solve for x:
x = 2 - 5y
Then we substitute this expression for x into the second equation and simplify:
y^2 + (2 - 5y) = y(2 - 4y)
Expanding and simplifying:
y^2 + 2 - 5y = 2y - 4y^2
Collecting like terms:
4y^2 - 6y + 2 = 0
Dividing by 2 to simplify:
2y^2 - 3y + 1 = 0
We can factor this quadratic equation as:
(2y - 1)(y - 1) = 0
So either 2y - 1 = 0 or y - 1 = 0, which gives:
y = 1/2 or y = 1
Substituting each value of y back into the equation 2 - x = 5y, we can solve for x:
If y = 1/2, then 2 - x = 5(1/2) = 5/2, so x = 2 - 5/2 = 3/2
If y = 1, then 2 - x = 5(1) = 5, so x = 2 - 5 = -3
Therefore, the solution to the system of equations is:
x = 3/2 and y = 1/2
OR
x = -3 and y = 1
Explanation: