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 t
Question 227223: 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 Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Three numbers, x, y, z
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Write an equation for each statement:
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"the sum of three numbers is -2."
x + y + z = -2
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"the sum of three times the first number, twice the second number, and the third number is 9."
3x + 2y + z = 9
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" the difference between the second number and half the third number is 10."
y - .5z = 10
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find the numbers:
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Multiply the last equation by 2 and add to the 1st equation
x + y + z = -2
0 + 2y -z = 20
---------------addition eliminates z
x + 3y = 18
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Add the same equation to the 2nd the equation
3x + 2y + z = 9
0 + 2y - z = 20
------------------eliminate z again
3x + 4y = 29
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Use these two 2 unknown equations to eliminate x
Multiply the 1st one by 3
3x + 9y = 54
3x + 4y = 29
--------------Subtraction eliminates x
0x + 5y = 25
y =
y = 5
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Using y - .5z = 10
5 - .5z = 10
-.5z = 10 - 5
z =
z= -10
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Find x using the 1st equation
x + 5 -10 = -2
x - 5 = -2
x = - 2 + 5
x = +3
:
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Check solutions in the 2nd equation
3x + 2y + z = 9
3(3) + 2(5) - 10 = 9; confirms our solution
