SOLUTION: The sum of three numbers is -2. The sum of three times the first number, twice the second number, and the third number is 9. The difference between the second number and half the

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Question 1132805: The sum of three numbers is -2. The sum of three times the first
number, twice the second number, and the third number is 9. The
difference between the second number and half the third number is 10.
Find the numbers.
What is the equation? I honestly have no clue how to get the equations but I can solve the equations with no problem.
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

let’s three numbers be ,, and

given:

The sum of three numbers is .
.....eq.1

The sum of three times the first number, twice the second number, and the third number is .
.....eq.2

The difference between the number and the number is .
........eq.3

solve the system:

.....eq.1
.....eq.2
........eq.3
__________________________

start with
........eq.3..solve for

............eq.3a

substitute in:..eq.1 and ..eq.2

.....eq.1.

....eq.1a

.....eq.2

.....eq.2a

from eq.1a and eq.2a, we have

....both sides multiply by

--------------------------

--------------------------subtract

go to ....eq.1a , plug in value

go to .....eq.3a , plug in value