Question 980439: The sum of three numbers is14. The second number is the result of subtracting the third from the first, and the third number is the sum of the second and seven times the first. Translate the problem into a system of three equations with three unknowns, and then solve the system to the numbers.
( you can use a method at your convenience to solve the system.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of three numbers is 14.
a + b + c = 14
The second number is the result of subtracting the third from the first,
b = a - c
We can rearrange this to
-a + b + c = 0
and the third number is the sum of the second and seven times the first.
c = b + 7a
Arrange to
-7a - b + c = 0
Using the 1st two equations
a + b + c = 14
-a +b + c = 0
-----------------subtraction eliminates b and c, find a
2a = 14
a = 7
:
using the 2nd and 3rd equations, replace a with 7
-7(7) - b + c = 0
-7 + b + c = 0
we have
- b + c = 49
+ b + c = 7
-----------------Adding eliminates b, find c
2c = 56
c = 28
Find b using the 1st equation
7 + b + 28 = 14
b = 14 - 35
b = -21
:
we have a = 7; b = -21; c + 28
:
:
Check in the 2nd and 3rd statement
"The second number is the result of subtracting the third from the first,
-21 = 7 - 28
the third number is the sum of the second and seven times the first.
28 = -21 + 7(7)
28 = -21 + 49
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