document.write( "Question 54320This question is from textbook mathematics in action
\n" ); document.write( ": Solve the system of equations algebrically.
\n" ); document.write( "Eliminate the z variable.\r
\n" ); document.write( "\n" ); document.write( "2x-y+4z=-2
\n" ); document.write( "3x-2y-z=-3
\n" ); document.write( "x+4y+2z=17 \n" ); document.write( "
Algebra.Com's Answer #36597 by funmath(2933)\"\" \"About 
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2x-y+4z=-2 (E1)
\n" ); document.write( "3x-2y-z=-3 (E2)
\n" ); document.write( "x+4y+2z=17 (E3)
\n" ); document.write( ": Eliminate z in (E1) and (E2) by multiplying 4*(E2) and adding the two equations.
\n" ); document.write( "2x-y+4z=-2----------> 2x- y+4z=-2
\n" ); document.write( "4(3x-2y-z)=4(-3)---->12x-8y-4z=-12
\n" ); document.write( ":
\n" ); document.write( " 2x- y+4z=-2
\n" ); document.write( "12x-8y-4z=-12
\n" ); document.write( "_____________
\n" ); document.write( "14x-9y+0z=-14
\n" ); document.write( "14x-9y=-14 (E4)
\n" ); document.write( ":Eliminate the z using 2*(E2) + (E3).
\n" ); document.write( "2(3x-2y-z)=2(-3)------->6x-4y-2z=-6
\n" ); document.write( "x+4y+2z=17-------------> x+4y+2z=17
\n" ); document.write( ":
\n" ); document.write( "6x-4y-2z=-6
\n" ); document.write( "+x+4y+2z=17
\n" ); document.write( "_____________
\n" ); document.write( "7x+0y+0z=11
\n" ); document.write( "7x=11
\n" ); document.write( "7x/7=11/7
\n" ); document.write( "x=11/7
\n" ); document.write( ":Substitute x=11/7 into (E4) and solve for y:
\n" ); document.write( "14(11/7)-9y=-14
\n" ); document.write( "\"154%2F7-9y=-14\" Clear the fraction by multiplying everything by 7 to make it easier to solve.
\n" ); document.write( "\"7%2A154%2F7%2B7%28-9y%29=7%28-14%29\"
\n" ); document.write( "\"cross%287%29154%2Fcross%287%29-63y=-98\"
\n" ); document.write( "154-63y=-98
\n" ); document.write( "-154+154-63y=-98-154
\n" ); document.write( "-63y=-252
\n" ); document.write( "-63y/-63=-252/-63
\n" ); document.write( "y=4
\n" ); document.write( ":
\n" ); document.write( "Substitute x=11/7 and y=4 into (E2).
\n" ); document.write( "3(11/4)-2(4)-z=-3
\n" ); document.write( "Work that out and you get z=-2/7
\n" ); document.write( "So your answer is (11/7,4,-2/7)
\n" ); document.write( "Don't forget to check your answer by sustituting these values into all three original equations.
\n" ); document.write( "Let me know if you need more explanation.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "
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