document.write( "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.
\n" ); document.write( "[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.] \n" ); document.write( "
Algebra.Com's Answer #101472 by ankor@dixie-net.com(22740)\"\" \"About 
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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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\n" ); document.write( "Let the 3 numbers be x, y, z
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\n" ); document.write( "Write an equation for each statement:
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\n" ); document.write( "\"If the second number is subtracted from the sum of the first number and 5 times the third number, the result is -25.\"
\n" ); document.write( "x + 5z - y = -25
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\n" ); document.write( "\"The third number plus 4 times the first number is -4.\"
\n" ); document.write( "z + 4x = -4
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\n" ); document.write( "\"The first number plus 4 times the second number plus the third number is 16.\"
\n" ); document.write( "x + 4y + z = 16
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\n" ); document.write( "Find the three numbers.
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\n" ); document.write( "Write the 3 equations in the standard form:
\n" ); document.write( "x - y + 5z = -25
\n" ); document.write( "4x +0y + z = -4
\n" ); document.write( "x + 4y + z = 16:
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\n" ); document.write( "Subtract the 3rd equation from the 2nd equation
\n" ); document.write( "4x + 0y + z = -4
\n" ); document.write( " x + 4y + z = 16
\n" ); document.write( "------------------Subtracting eliminates z
\n" ); document.write( "3x - 4y + 0 = -20
\n" ); document.write( "3x - 4y = -20
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\n" ); document.write( "Multiply the 2nd equation by 5, subtract the 1st equation:
\n" ); document.write( "20x + 0y + 5z = -20
\n" ); document.write( " x - 1y + 5z = -25
\n" ); document.write( "---------------------subtracting eliminates z
\n" ); document.write( "19x + y + 0 = +5
\n" ); document.write( "19x + y = +5
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\n" ); document.write( "Multiply the above equation by 4 and add to the 1st \"two unknown\" equation:
\n" ); document.write( "3x - 4y = +20
\n" ); document.write( "76x +4y = -20
\n" ); document.write( "----------------adding eliminates y
\n" ); document.write( "79x + 0y = 0
\n" ); document.write( "x = 0
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\n" ); document.write( "This makes it easy to find z using the 2nd equation:
\n" ); document.write( "z + 4(0) = -4
\n" ); document.write( "z = -4
\n" ); document.write( ":
\n" ); document.write( "Use the 1st equation to find y:
\n" ); document.write( "x + 5z - y = -25
\n" ); document.write( "0 + 5(-4) - y = -25
\n" ); document.write( "-20 - y = 025
\n" ); document.write( "-y = -25 + 20
\n" ); document.write( "-y = -5
\n" ); document.write( "y = +5:
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\n" ); document.write( "We have x=0; y=5; z=-4
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\n" ); document.write( "Check solutions in the 3rd equation
\n" ); document.write( "x + 4y + z = 16
\n" ); document.write( "0 + 4(5) - 4 = 16; confirms our solutions \n" ); document.write( "
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