For the system of linear equations x/3-y/5=4 and 3x/4+2y/3=6,how many solutions exist?

A system of two linear equations has only 3 possible
outcomes:

* no solution

* 1
solution

* infinite
solutions

You can tell which of these is correct by
graphing.  If the lines are parallel, then there is no solution.  If the lines intersect
at one point, then there is one solution.  If the lines coincide, then there are
infinite solutions.

 x/3-y/5=4 and
3x/4+2y/3=6

First, rewrite equation in slope-intercept
form.

x/3 - y/5 =
4

y = 5(x/3 -
4)

3x/4 + 2y/3 =
6

y = 3/2(6 -
3x/4)

Now graph the two
equations.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-1,12,-5,1,1,1,1,1,1,300,200,func,5(x/3-4),null,0,0,,,black,1,none,func,(3/2)(6-3x/4),null,0,0,,,black,1,none"/>

The
lines intersect at exactly one point, therefore this system has one
solution.