Question 383271: The following is known about three numbers:If the second number is subtracted from the sum of the first number and 4 times the third number, the result is 9. 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 -14. Find all three numbers.
(Let x represent the first number,y the second number,and z the third number. Use the given conditions to solve a system of equations.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The following is known about three numbers:
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Write an equation for each statement:
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If the second number is subtracted from the sum of the first number and 4 times the third number the result is 9.
x - y + 4z = 9
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The third number plus 5 times the first number is 1.
5x + z = 1
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The first number plus 3 times the second number plus the third number is -14.
x + 3y + z = -14
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Find all three numbers.
:
We can use elimination here:
Multiply the 1st equation by 3, add to the 3rd equation
3x - 3y + 12z = 27
x + 3y + z = -14
----------------------adding eliminates y
4x + 13z = 13
I think this tells us that x = 0, z = 1, but let's see
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Multiply the 2nd equation by 13, subtract the above equation
65x + 13z = 13
4x + 13z = 13
---------------- subtraction eliminates z
61x = 0
x = 0
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Find y
x - y + 4z = 9
0 - y + 4(1) = 9
-y = 9 - 4
-y = 5
y = -5
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Solution: x=0, y=-5, z= 1
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Check in the 3rd equation
x + 3y + z = -14
0 + 3(-5) + 1 = -14
-15 + 1 = -14
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