SOLUTION: Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number.

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Question 417857: Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first number and the third number. what are the 3 numbers?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the numbers be x, y, z
2x=y+z+11
2x-y-z=11
2x+3z=y+1
2x-y+3z=1
y=x+z
-x+y-z=0
2x-y-z=11-------------- 1
2x-y+3z =1--------------2
-x+y-z= 0-------------- 3

consider equation 1 &2
Multiply 1 by -1
Multiply 2 by 1
we get
-2x+y+z =-11
2x-y+3z =1
Add the two
4z=-10 -------------4
z==-2.5
consider equation 2 & 3
Multiply 2 by 1
Multiply 3 by 1
we get
2x-y+3z =1
-x+y+-z =0
Add the two
1x+2z= 1-------------5
plug value of z
x-5=1
x=6
plug value of x & z in 1
12-y+2.5=11
y=3.5