lOO AlvGEBRA. 



Suppose x—vy, where 2> is a new unknown quantity. Then, 

 substituting this in the equations, the system becomes 



3^'y—ioy-=^S' (4)) * ^ 



From equation (t,) we find that 



and from equation (4^) 



yc^'— 16 



r=-^^, (6) 



Whence, from (5J and (6) 



5 35 



Z^""-— 2 27 327'— 10. 



Clearing of fractions, 



152^^— 50=352'=— 7oz\ 

 Transposing and uniting terms, and dividing through by 10 



2v—7Z'=-s. 

 Solving this quadratic 



z'=f or T. 

 Substituting the first of these values in ('3 j we obtoin 



Whence- jj/==b2 



and since x=7'y 



Now, substituting the second value of z> in (2,) we obtain 



y—2x=s- 

 Whence y= ± \/ — 5 



and, since x=vy, 



x=d=V— 5- 

 Therefore we have, as the solution of the original system, the 

 four sets of values. 



-^=5, 7=2; -^= — 5, J'= — 2; x=\/ — s, y=^\^ — 5> 

 x= — \/—s, J= — V— 5- 

 The general system of twojequations of the above class may be 

 represented by 



x^-^axj-j-d^'''=c \ /, J 



x'-i-dxj-\-ey=/.}' '^ 



