If x + y = 7 and xy = 4, then find the value of x^2 + y^2.

X+y=7
xy=4

in xy=4, divide both sides by any variable (lets say i divide it y y)
xy=4
x=4/y
Now substitute it to the 1st equation
x+y=7
4/y+y=7
Multiply both sides by y
4+y^2=7y
Change to standard form
y^2-7y=4
Use the square of something...
y^2-7y+49/4=4+49/4
(y+7/2)^2=65/4
Squareroot both sides
y+7/2=posinega(sqrt of 65)/2
y=(sqrt of 65)/2-7/2
or y=-(sqrt of 65)/2-7/2