SOLUTION: the following is known about three numbers: if the second number is subtracted from the sum of the first number and 5 times the third number, the result is -7. the third number plu
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Question 203642: the following is known about three numbers: if the second number is subtracted from the sum of the first number and 5 times the third number, the result is -7. the third number plus 5 times the first number is -1. the first number plus 3 times the second number plus the third number is 5. find the three numbers.
[hint: let x represent the first number, y the second number, and z the third number. use the given conditions to write and solve a system of equations.]
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the following is known about three numbers: x, y, z
if the second number is subtracted from the sum of the first number and 5 times the third number, the result is -7.
(x+5z)-y = -7
----------------------
the third number plus 5 times the first number is -1.
z+5x = -1
----------------------
the first number plus 3 times the second number plus the third number is 5. find the three numbers.
x+3y+z = 5
------------------------------------
Rearrange to get:
x - y + 5z = -7
5x + 0y +z = -1
x + 3y + z = 5
-------------------
Multiply thru the 1st equation by 3
3x - 3y + 15z = -21
-----
Add that to the 3rd equation to get:
4x +16z = -16
----
Group that with the 2nd equation to solve for x and z:
5x + z = -1
4x +16z = -16
----------------------
Multiply thru the 1st equation by 16; then solve for "x":
80x + 16z = -16
4x + 16z = -16
----------------------
Subtract the 2nd from the 1st to get:
76x = 0
x = 0
---
Substitute that into 4x+16z = -16 to get:
z = -1
-------------------
Substitute those values into x-y+5z = -7 to solve for "y":
0 -y +5(-1)=-7
-y-5=-7
-y = -2
y = 2
------------------
x = 0
y = 2
z = -1
------------
Cheers,
Stan H.
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