The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. they hope to sell all of the shirts they ordered, to earn a total of $1,750. after the first week of the fundraiser, they sold   1/3 of the short-sleeved shirts and   1/2of the long-sleeved shirts, for a total of 100 shirts. this system of equations models the situation.     5x + 10y = 1,750 1/3x +  1/2y = 100 let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. how many short-sleeved shirts were ordered? how many long-sleeved shirts were ordered?

150 short-sleeved shirts and 100 long-sleeved shirts.

Step-by-step explanation:

We will use elimination to solve this system of equations.  We will make the coefficients of x the same in order to eliminate them; to do this, we must multiply the bottom equation by 15 (1/3 of 15 is 5, so 15(1/3) = 5):

Subtract the second equation from the first one:

Divide both sides by 2.5:

2.5y/2.5 = 250/2.5

y = 100

Substitute 100 in for y in the first equation:

5x+10(100) = 1750

5x+1000 = 1750

Subtract 1000 from both sides:

5x+1000 - 1000 = 1750 - 1000

5x = 750

Divide both sides by 5:

5x/5 = 750/5

x = 150

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0