(1)
abx+b2y=ab-b2,
abx-a2y=a2+ab,
(a2+b2)y=-(a2+b2), y=-1;
bx+a=a+b, x=1. SOLUTION x=1, y=-1.
(2)
abx+b2y=bc,
abx+a2y=a+ac,
(b2-a2)y=bc-a-ac, y=(bc-a-ac)/(b2-a2) or (a+ac-bc)/(a2-b2).
a2x+aby=ac,
b2x+aby=b+bc,
(a2-b2)x=ac-b-bc, x=(ac-b-bc)/(a2-b2) or (b+bc-ac)/(b2-a2).
(3)
bx-ay=0,
ax+by=a2+b2,
b2x-aby=0,
a2x+aby=a3+ab2,
(a2+b2)x=a3+ab2, x=a;
a2+by=a2+b2, y=b. SOLUTION; x=a, y=b.
(4) (ambiguous)
ay-bx=0, ay=bx, x=ay/b, 1/x=b/(ay),
ab2/x+a2b=a2+b2
(b/(ay))(ab2)+a2b=a2+b2,
b3/y+a2b=a2+b2,
b3/y=a2+b2-a2b,
y=b3/(a2+b2-a2b).