SOLUTION: Six times the difference of two positive numbers exceeds 4 by 21. Three times their sum equals 8 times the smaller number. Find the numbers.

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Question 697603: Six times the difference of two positive numbers exceeds 4 by 21. Three times their sum equals 8 times the smaller number. Find the numbers.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Six times the difference of two positive numbers x and y ( let y be smaller number) exceeds 4 by 21.
6%28x-y%29%2B21=4.....1

Three times their sum equals 8 times the smaller number
3%28x%2By%29=8y.......2
now we have system to solve:

6%28x-y%29%2B21=4.....1
3%28x%2By%29=8y.......2
_________________________

6x-6y=4-21.....1.....solve for x
6x=6y-17
x=6y%2F6-17%2F6
x=y-2.833....plug in 2
3%28y-2.833%2By%29=8y.......2....solve for y
3y-8.499%2B3y=8y
6y-8.499=8y
-8.499=8y-6y
-8.499=2y
-4.2495=y
now find x
x=-4.2495-2.833
x=-7.0825
check:
6%28-7.0825-%28-4.2495%29%29%2B21=4.....1
6%28-7.0825%2B4.2495%29%2B21=4
6%28-2.833%29%2B21=4
-16.998%2B21=4
4.002=4
4=4