SOLUTION: hello, I need to know how to solve: For what value(s) of C does 3x-4y=9 and 12x-16y=c have infinite solutions? Thank you

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: hello, I need to know how to solve: For what value(s) of C does 3x-4y=9 and 12x-16y=c have infinite solutions? Thank you       Log On


   

Question 72425: hello, I need to know how to solve:
For what value(s) of C does 3x-4y=9 and 12x-16y=c have infinite solutions?
Thank you
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
For two lines to have an infinite number of soulutions, they have to, in reality, be the same line.
Start with your first equation:
+3x-4y=9+
This is written in standard form
+Ax+%2B+By+=+C+
Now look at your second equation:
+12x-16y=c+
It too is in Standard form.
Look at the 'A' Values of each. The 2nd is 4-times the first.
Look at the 'B' Values of each. The 2nd is 4-times the first.
So, that means that the 'C' values are in the same ratio or proportion.
9 * 4 = 36
Your vallue for 'C' in the 2nd equation is 36.