THE LARGER NUMBER IS 52, WHILE THE SMALLER NUMBER IS 31.
solution
let assume the smaller to be y
let assume the larger number to be x
x + y = 83 ------------1
2x + 3y = 197...........2
using simultaneous equation
make x the subject of formular in equation 1
x=83 - y .................3
substitute equation 3 in equation 2
any where you see x replace it with 83-y in equation 2
2(83 - y) + 3y = 197
open the bracket by multiplying by 2 by the content of the bracket
166 - 2y + 3y = 197
-2y +3y = y
therefore:
166 + y = 197
collect like terms by taking 166 to the lefthand side of the equation
y = 197 - 166
y = 31.
substitute y in equation 2 above
x + 31 = 83
collect like terms by taking 31 to the lefthand side of the equation
x = 83 - 31
x = 52
X represent the larger number which is 52
Y represent the lsmaller number which is 31