Keep working on it,

it's 1.30 am here, so it's my naptime.

Remember the following though.

When you write the equation of a line, the x and y values are the co-ordinates of all of the points on the line.

A different x will go with a different y.

When you have 2 line equations, as in these cases,

once you solve the simultaneous equations,

you find the only point on both lines, because only those x and y co-ordinates are on both lines.

This is why you need to first write the equations of the lines that the orthocentre and circumcentre are on, before you solve the simultaneous equations.