SOLUTION: Find two numbers such that twice the first exceeds three times the second by 1, and three times the first exceeds twice the second by 14.

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Question 157926: Find two numbers such that twice the first exceeds three times the second by 1, and three times the first exceeds twice the second by 14.
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
Let x -----> 1st number
y ----------> 2nd number
1st condition:
2x=3y%2B1 --------> eqn 1: twice the 1st exceeds 3 times the second by 1
3x=2y%2B14 -------> eqn 2: 3 times the 1st exceeds twice the 2nd by 14
In eqn 1 we get,
x=%283y%2B1%29%2F2 ------> eqn 3
Put eqn 3 to eqn 2:
%283%29%2A%28%283y%2B1%29%2F2%29=2y%2B14, cross multiply
%282%29%282y%2B14%29=%283%29%283y%2B1%29
4y%2B28=9y%2B3
28-3=9y-4y
25=5y -------> cross%2825%295%2Fcross%285%29=cross%285%29y%2Fcross%285%29
y=5, ANSWER
In eqn 3:
x=%28%283%2A5%29%2B1%29%2F2=%2815%2B1%29%2F2=16%2F2
x=8, ANSWER
In doubt? go back eqn 1& 2:
via eqn 1: %282%29%288%29=%283%29%285%29%2B1
16=15%2B1
16=16
via eqn 2: %283%29%288%29=%282%2A5%29%2B14
24=10%2B14
14=14
Thank you,
Jojo