Hal has enough clay to make $24$ small vases or $6$ large vases. In other words, the large vases require $4$ times the amount of clay as the small ones. He only has enough of a special glazing compound to glaze $16$ of the small vases or $8$ of the large vases.

Let $x_1=$ the number of small vases and $x_2=$ the number of large vases.

The smaller vases sell for $$3$ each, while the larger vases would bring $$9$ each.