SOLUTION: How many solutions exist for the following system of equations? -10x – 10y = 20 -10x + 6y = -108

Algebra ->  Systems-of-equations -> SOLUTION: How many solutions exist for the following system of equations? -10x – 10y = 20 -10x + 6y = -108      Log On


   

Question 762715: How many solutions exist for the following system of equations?
-10x – 10y = 20
-10x + 6y = -108
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given
(1) -10x -10y = 20 and
(2) -10x +6y = -108
Now subtract (2) from (1) and get
(3) (-10x -10y) - (-10x +6y) = 20 - (-108) or
(4) -16y = 128 or
(5) y = -8
Then from (1) we get
(6) -10x -10(-8) = 20 or
(7) -10x = 20 -80 or
(8) -10x = -60 or
(9) x = 6
Let's check this with (2).
Is (-10*6 + 6*(-8) = -108)?
Is (-60 - 48 = -108)?
Is (-108 = -108)? Yes
Answer: The system of equations has one solution at the point (6,-8).