SOLUTION: I am doing my end of course review for my final and I understand all of it except 2 questions both similar. I will place one of them below and hopefully with your help I will be ab

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I am doing my end of course review for my final and I understand all of it except 2 questions both similar. I will place one of them below and hopefully with your help I will be ab      Log On


   

Question 875357: I am doing my end of course review for my final and I understand all of it except 2 questions both similar. I will place one of them below and hopefully with your help I will be able do the other one on my own. Thank you SOOO much in advance. -- Alex C
Problem-
Which of the linear systems has exactly one solution?
A) 5x + 3y = -22 B) 2x + 3y = 45
4x - 5y = 12 2y + 4/3x = 30
C) 2x - 3y = -15 D) x + y = 2
2/3x - y = 3 1/2x + 1/2y = 1
(Sorry for any typos I'm on my ipad)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2x - 3y = -15
2x-3y-15=0: let this represent a1x+b1y+c1
a1=2,b1=-3c1=-15

x + y = 2 :
x+y-2=0 : let this represent a2x+b2y+c2=0
a2=1, b2=1,c2=-2
if a1/a2 not equal to b1/b2 then the system has one solution
in the above problem
2/1 = not equal to 1/1
hence has a unique solution