Question 139017: 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 -25. The third number plus of 4 times the first number is -4. The first number plus 4 times the second number plus the third number is 16. 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 ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 -25. The third number plus of 4 times the first number is -4. The first number plus 4 times the second number plus the third number is 16. Find the three numbers.
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Let the 3 numbers be x, y, z
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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 5 times the third number, the result is -25."
x + 5z - y = -25
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"The third number plus 4 times the first number is -4."
z + 4x = -4
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"The first number plus 4 times the second number plus the third number is 16."
x + 4y + z = 16
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Find the three numbers.
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Write the 3 equations in the standard form:
x - y + 5z = -25
4x +0y + z = -4
x + 4y + z = 16:
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Subtract the 3rd equation from the 2nd equation
4x + 0y + z = -4
x + 4y + z = 16
------------------Subtracting eliminates z
3x - 4y + 0 = -20
3x - 4y = -20
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Multiply the 2nd equation by 5, subtract the 1st equation:
20x + 0y + 5z = -20
x - 1y + 5z = -25
---------------------subtracting eliminates z
19x + y + 0 = +5
19x + y = +5
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Multiply the above equation by 4 and add to the 1st "two unknown" equation:
3x - 4y = +20
76x +4y = -20
----------------adding eliminates y
79x + 0y = 0
x = 0
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This makes it easy to find z using the 2nd equation:
z + 4(0) = -4
z = -4
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Use the 1st equation to find y:
x + 5z - y = -25
0 + 5(-4) - y = -25
-20 - y = 025
-y = -25 + 20
-y = -5
y = +5:
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We have x=0; y=5; z=-4
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Check solutions in the 3rd equation
x + 4y + z = 16
0 + 4(5) - 4 = 16; confirms our solutions
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