SOLUTION: The sum of two numbers is 43. Twice the larger number exceeds three times the smaller numner by 16. Find the number

Question 181261: The sum of two numbers is 43. Twice the larger number exceeds three times the smaller numner by 16. Find the number
Answer by eperette(173) (Show Source): You can put this solution on YOUR website!
x + y = 43
2y = 3x + 16
*****
x + y = 43
x +-x + y = 43 -x
0 + y = 43 - x
y = 43 - x
2y = 3x + 16
2(43 - x) = 3x + 16
2(43) + 2(-x) = 3x + 16
86 - 2x = 3x + 16
86 - 2x + 2x = 3x + 2x + 16
86 - 0 = 5x + 16
86 - 16 = 5x + 16 - 16
70 = 5x + 0
70/5 = 5x/5
14 = x
then
y = 43 -x
y = 43 - 14
y = 29
>>>>>>>CHECK>>>>>>
14 + 29 = 43
2(29)= 58
3(14)= 42
58 - 42 = 16
RIGHT
so the smallest number x=14 and the larger number y=29
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