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.
