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Challenge 398: Squarely Simultaneous

Here's a pair of uncommon simultaneous equations to solve...

 (i) Given that 15x2 - 18xy + 3y2 = a(bx-y)2 - c(x + y)2 for all values of x and y, determine the values of a, b and c.

(ii) Find all pairs of values (x, y) that satisfy the simultaneous equations

(1) 15x2 - 18xy + 3y2 = 0

(2) 10x2 - 16xy + y2  + 5 = 0