SOLUTION: the sum of three numbers is 20. if we multiply the first number by 2, add the second number to the result and subtract the third number, we get 23. by adding second and third numbe

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Question 694515: the sum of three numbers is 20. if we multiply the first number by 2, add the second number to the result and subtract the third number, we get 23. by adding second and third numbers to 3 times the first number we get 46. what are the numbers?
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y+Z=20
2X+Y-Z=23
3X+Y+Z=46 ADD THE SECOND & THIRD EQUATIONS.
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5X+2Y=69
ADD THE FIRST & SECOND EQUATIONS.
X+Y+Z=20
2X+Y-Z=23
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3X+2Y=43 NOW ADD THIS EQUATION TO THE PREVIOUS SUM TIMES -1.
-5X-2Y=-69
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-2X=-26
X=-26/-2
X=13 ANS.
5*13+2Y=69
65+2Y=69
2Y=69-65
2Y=4
Y=4/2
Y=2 ANS.
13+2+Z=20
15+Z=20
Z=20-15
Z=5 ANS.
PROOF:
2*13+2-5=23
26-3=23
23=23