Question 652169
Joe buys five shirts and three shorts for $51.
Bill buys three shirts and seven shorts for $80.
How much does each shirt and each pair of shorts cost.
So, if x is cost of each shirt
And if y is the cost of each pair of shorts
.
gives you the "system of equations":
5x + 3y = 51  
3x + 7y = 80
solve by the "addition method".  
multiply top eq by 3 and bottom eq by -5 then combine both:
 15x + 9y = 153  
-15x -35y =-400
----------------
     -26y = -247
        y = $9.50 (shorts)
.
shirts:
5x + 3y = 51  
5x + 3(9.50) = 51  
5x + 28.50 = 51  
5x = 22.50
x = $4.50