y = x² - 5x + 1
x + y = -2
substitute the first equation into the second one....
x + x² - 5x + 1 = -2
x² - 4x + 1 = -2
add 2 on both sides to make the equation equal to 0.
x² - 4x + 3 = 0
factor this.
(x - 1)(x - 3) = 0
x = 1 , x = 3
to find the y values, you would have to substitute x = 1 and x = 3.
1 + y = -2 3 + y = -2
y = -3 y = -5
So your answers are
x = 1 , x = 3
y = -3, y = -5
Hope this helped!