Question 74678
Let L=# of large animals and s=# small animals (it's easier to recognize L and s compared to x and y). Since we know they ordered 450 pieces of both large and small animals the first equation looks like 
{{{L+s=450}}}
And since the total price is $7,320 it is
{{{20L+14s=7320}}} the number of animals multiplied by their respective prices add up to the total.
{{{L=s-450}}}Solve for L. Plug this ito {{{20L+14s=7320}}}
{{{20(450-s)+14s=7320}}}
{{{-20s+9000+14s=7320}}}
{{{-6s+9000=7320}}}
{{{-6s=-1680}}}
{{{s=280}}}
So they ordered 280 small animals. Use this to solve for L
{{{(280)+L=450}}}
{{{L=450-280}}}
{{{L=170}}}
So they ordered 170 large animals. 

<p>
Check:
{{{L+s=450}}}
{{{20L+14s=7320}}}
Plug in L=170 and s=280
{{{170+280=450}}}
{{{20(170)+14(280)=7320}}}

We can see the values satisfies the system of equations:
{{{450=450}}}works
{{{7320=7320}}}works


Here's another way to do it
*[invoke linear "L", "s", 1, 1, 450, 20, 14, 7320 ]