All sweater sold at a fixed price all shirts sold at a fixed price. one sweater and four shirts cost $46, while four sweaters and five shirts cost $96,

Let the cost of sweater be x. Let the cost of shirt be y.

1 sweater and 4 shirts = 1*x + 4*y = x + 4y = $46

4 sweaters and 5 shirts = 4*x + 5*y = 4x + 5y = $96

x + 4y = 46(a)

4x + 5y =96(b)

Multiply equation (a) by 4

4*(x + 4y) = 4*46

4x +16y = 184 (c)

4x + 5y =  96(b)      Equation c - Equation b, inorder to eliminate x.

0x + 11y = 88

11y = 88

y = 88/11 = 8

But from a :    x  + 4y = 46       x + 4*8 = 46

x + 32 = 46

x = 46 - 32 = 14

Hence the cost of a sweater, x, is $14 and a shirt, y, is $8 

Hope this helped.