Question 72425
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 + 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.