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

1 Answer
Sittun Swayam P.
Nov 14, 2015

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−x−2y = 1 => -x=1+2y−x=1+2y => x=-(1+2y)x=−(1+2y) ----EQUATION 1
  2. 9x-y=-19x−y=−1 => 9x=y-19x=y−1 => x=1/9*(y-1)x=19⋅(y−1) ----EQUATION 2

Equating the values of x from EQUATION 1 and EQUATION 2;
we have;
-(1+2y)=1/9*(y-1)−(1+2y)=19⋅(y−1)
=> -9-18y=y-1−9−18y=y−1
=>-18y-y=-1+9−18y−y=−1+9
=>-19y=8−19y=8
=>y=-8/19y=−819

Using EQUATION 1;
x=-(1+2y)x=−(1+2y)
=>x=-(1+2*(-8/19))x=−(1+2⋅(−819))
=>x=-(1-16/19)x=−(1−1619)
=>x=-3/19x=−319

So there you have it!!

x=-3/19x=−319
and
y=-8/19y=−819

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