40 
[39 ! 
391. 
SOLUTION OF A PBOBLEM OF ELIMINATION. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. yiii. (1867), 
pp. 183—185.] 
It is required to eliminate x, y from the equations 
This system may be written 
if for shortness 
Or putting 
we have 
X 4 
py, 
x l y\ 
xy 3 , 
y* 
a , 
b , 
c , 
d , 
e 
a , 
b' , 
C , 
d', e' 
a", 
b", 
c" , 
d", e" 
= 0. 
x 4 = X\a, 
a?y = XXb, 
x-y 1 = £Xc, 
x y s = 2Xd, 
f = SXe; 
SXtt = \a q- X a q-X a , &c. 
x — k 
y~~ ’ 
2X (a + A;6) = 0, 
SX (6 q- /cc) = 0, 
Sx (c q- M) = 0, 
2X(eZ q- &e) = 0;