Multiply  or  divide  the  equations,  if  necessary  ,  in  such  a
manner  that  the  term  which  contains  one  of  the  unknown  quan-
tities shall  be  the  same  in  both.
Then  subtract  one  equation  from  the  other,  if  the  signs
of  this  unknown  quantity  are  alike,  or  add  them  together,  if
the  signs  are  unlike.
N.  B.  It  must  be  kept  in  mind  that  both  members  of  an
equation  are  always  to  be  increased  or  diminished  alike,  iri
order  to  preserve  their  equality.
Prob.  20.  Given  2z-Hy=20  >  ^

J*  >  To  find  the  value  of  x  and  y.
And     4z--5:=r28  )


1.  Mult,  the  1st  equation  by  2,     4z+8y=40

2.  The  2d  equation  is  4z+5y=:28
Subtracting  the  2d  from  the  1st,  3^=12
Dividing,  &c.  y—  4  ;  and  z—  2.
QUEST.  —  What  is  the  third  method  of  extermination  called  ?  What  is
the  rule?  What  is  the  object  of  multiplying  the  equation  by  a  certain
quantity  ?  How  do  you  know  when  to  add  and  when  to  subtract  ?


178  ALGEBRA.  [Sect.  XI.
Prob.  21.  Given  2x+y=l6  )  ™    ~    , ,,

And     3z  -  %=6  I  T°  find  the  ValUG  °f  X  and  y'
Prob.  22.  Given  4x+3^50  |  TQ  fim]  ^  yalue  of    ^

And  3x— %=  6  J

Prob.  23.  Given  3z4-2y— 38  )  ™    c    , .,        ,        f        A

y  >  To  find  the  value  of  x  and  y.
And    5z+4y=68  J

Prob.  24.  Given  4z— 40= — 4y  )  ™    ,.    .  ,

2*  >  To  find  the  val.  of  x  and  y.
