How do you solve the following system?: #-x -2y =1, 9x -y = -1#

1 Answer
Nov 14, 2015

Answer:

We can solve this question by finding the value of x with respect to y from both equations. Since the value of x should be equal, the equations thus obtained can be solved for y. And then either of the initial equations can be used to find x.

Explanation:

  1. #-x-2y# = 1 => #-x=1+2y# => #x=-(1+2y)# ----EQUATION 1
  2. #9x-y=-1# => #9x=y-1# => #x=1/9*(y-1)# ----EQUATION 2

Equating the values of x from EQUATION 1 and EQUATION 2;
we have;
#-(1+2y)=1/9*(y-1)#
=> #-9-18y=y-1#
=>#-18y-y=-1+9#
=>#-19y=8#
=>#y=-8/19#

Using EQUATION 1;
#x=-(1+2y)#
=>#x=-(1+2*(-8/19))#
=>#x=-(1-16/19)#
=>#x=-3/19#

So there you have it!!

#x=-3/19#
and
#y=-8/19#