Solve the curve xy=2 and x+y=3

This question is a simultaneous equation, this means we substitute one value into the other equation.We are looking for the points where the curves intersect.First I would take x+y=3 and bring the y over to the other side. x=3-ySubstitute this into the other curve. (3-y)y=2 and multiply through everything to give y² -3y+2=0Factorise this to give (y-2)(y-1)=0 and subsequently the values y=1 y=2. The Y coordinates of where the curves touchsubstitute this back into the initial curves to work out the x coordinates.This gives the coordinates of intersection of (2,1) (1,2)