SOLUTION: Hi! Sorry I put the wrong email!! I have a question for my college algebra class. The problem says: Show that the equations in exercise 13 are inconsistent if a1/a2=b1/b2does n

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hi! Sorry I put the wrong email!! I have a question for my college algebra class. The problem says: Show that the equations in exercise 13 are inconsistent if a1/a2=b1/b2does n      Log On


   

Question 1127801: Hi!
Sorry I put the wrong email!! I have a question for my college algebra class. The problem says:
Show that the equations in exercise 13 are inconsistent if a1/a2=b1/b2does not equal c1/c2
exercise 13 says show that the equations a1x+b1y=c1 & a2x+b2y=c2 are dependent if a1/a2=b1/b2=c1/c2. (Hint; let the value of this common ratio be k)
Thank you,
Maddie
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +a%5B1%5Dx+%2B+b%5B1%5Dy+=+c%5B1%5D+
(2) +a%5B2%5Dx+%2B+b%5B2%5Dy+=+c%5B2%5D+


If +a%5B1%5D%2Fa%5B2%5D+=+b%5B1%5D%2Fb%5B2%5D+=+k+%3C%3E+c%5B1%5D%2Fc%5B2%5D+ then +a%5B1%5D+=+ka%5B2%5D+, +b%5B1%5D=kb%5B2%5D+ and (1) can be rewritten

+ka%5B2%5Dx+%2B+kb%5B2%5Dy+=+c%5B1%5D+

Dividing by k:
(1') ++a%5B2%5Dx+%2B+b%5B2%5Dy+=+c%5B1%5D%2Fk+

So if +%28c%5B1%5D%2Fc%5B2%5D%29+%3C%3E+k+ (—> +%28c%5B1%5D%2Fk%29+%3C%3E+c%5B2%5D+ ), then the left hand sides of (1') and (2) are equal but the right hand sides have different quantities.

Therefore the system is inconsistent.