In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. if one sweater and four shirts cost $45, while four sweaters and five shirts cost $92, find the price of one sweater and the price of one shirt.

Say SH is the shirt cost and SW is the sweater cost: 
SW + 3SH = 42 
3SW+2SH = 56 

Solve the first for SW: 
SW = 42-3SH 

Plug that into the second: 
3(42-3SH) +2SH = 56 

Simplify: 
126 - 9SH +2SH = 56 
70 = 7SH 
SH = 10 

Plug this back into the SW formula: 
SW = 42 - 3SH = 42 - 3*10 = 12 

Shirts cost $10, sweaters cost $12.