' •-î- - 
30 
and moreover 
NOTE ON A SYSTEM OF ALGEBRAICAL EQUATIONS. 
[492 
/ \ / so %bx- a 4- ba? 1 . 
(*-y)(*-z) = ^ + 5T ^+ FT ^, =j^(“ + ^ + «*) = 0, 
so that x = y or else x = z. If x = z, the three equations reduce themselves to the two 
a + bx 2 +2y ,bx + y 2 (b + cx 2 ) = 0, 
a + 4 + c^r 4 =0, 
giving y = x, or else y = i — ; and it hence appears that if from this last 
0 “T" CX'' 
equation and a + 4bx" + c« 4 = 0 we eliminate x, the result must be a + 4by 2 + cy 4 = 0. 
For in the same way that the elimination of y, z from the original three equations 
gives a + 4bx 2 + cx* = 0, the elimination of x, z from the same three equations will give 
a + 4by” + cy 4, = 0, so that in any case y is a root of this equation. 
r T