document.write( "Question 72918: Solve the following:\r
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Algebra.Com's Answer #52276 by rmromero(383)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "Solve the following:\r
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document.write( "3x-5y+2z=19
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document.write( "5x+2y-3z=-8
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document.write( "-2x+3y+5z=7\r
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document.write( "To solve for systems of 3 linear equation in 3 variable, we use Substitution
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document.write( "Method, Elimination Method, Gaussian Reduction method, Cramer's rules.\r
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document.write( "I choose Elimination Method\r
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document.write( "equation 1 :      3x-5y+2z=19
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document.write( "equation 2 :      5x+2y-3z=-8
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document.write( "equation 3 :      -2x+3y+5z=7\r
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document.write( "Let us Eliminate x in equation 1 and equation 2.\r
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document.write( "              3x-5y+2z=19
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document.write( "              5x+2y-3z=-8
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document.write( "             _____________\r
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document.write( "Since we cannot eliminate 3x and 5x by adding, we will find a certain
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document.write( "number to that will be multiplied to the two equations.\r
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document.write( "Multiply 5 to 3x-5y+2z=19 and -3 to 5x+2y-3z=-8\r
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document.write( "               5(3x-5y+2z=19)
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document.write( "              -3(5x+2y-3z=-8)
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document.write( "             _________________\r
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document.write( "             15x - 25y +10z = 95
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document.write( "            -15x -  6y + 9z = 24    Add
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document.write( "                 - 31y + 19z = 119      Equation 4\r
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document.write( "Now eliminate x in equation 1 and equation 3. Multiply 2 to 3x-5y+2z=19
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document.write( "and 3 to -2x+3y+5z=7\r
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document.write( "             2(3x-5y+2z=19)
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document.write( "             3(-2x+3y+5z=7)
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document.write( "             ______________\r
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document.write( "             6x - 10y +  4z = 38
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document.write( "            -6x +  9y + 15z = 21
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document.write( "                   -y + 19z = 59   Equation 5\r
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document.write( "Then using equation 4 and equation 5 eliminate another variable.
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document.write( "I choose z then solve for y.\r
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document.write( "              -31y + 19z = 119      
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document.write( "          -1(  - y + 19z = 59  )
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document.write( "          ______________________\r
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document.write( "             -31y + 19z = 119  
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document.write( "                y - 19z = -59  
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document.write( "              -30y     = 60    
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document.write( "                     y = -2\r
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document.write( "The value of y will be substituted to either equation 5 or 4
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document.write( "I choose equation 5\r
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document.write( "               -y + 19z = 59, y = -2
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document.write( "            -(-2) + 19z = 59  
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document.write( "                    19z = 59 - 2
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document.write( "                    19z = 57          Divide 19 both sides
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document.write( "                      z = 3\r
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document.write( "The Substitute y = -2, z = 3 to equation 1 or 2 or 3.
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document.write( "I choose equation 3.\r
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document.write( "                -2x + 3y + 5z = 7, y = -2, z = 3
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document.write( "           -2x + 3(-2) + 5(3) = 7
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document.write( "                 -2x - 6 + 15 = 7
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document.write( "                          -2x = -2
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document.write( "                            x = 1\r
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document.write( "Checking: 
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document.write( "equation 1 :      3x-5y+2z=19, x = 1, y = -2, z = 3
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document.write( "                  3(1)-5(-2)+2(3)=19
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document.write( "                      3 + 10 + 6 = 19
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document.write( "                              19 = 19  ---------->True\r
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document.write( "equation 2 :      5x+2y-3z=-8, x = 1, y = -2, z = 3
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document.write( "                  5(1)+2(-2)-3(3)=-8
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document.write( "                       5 - 4 - 9 = -8
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document.write( "                              -8 = -8 ------------>True\r
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document.write( "equation 3 :       -2x+3y+5z=7, x = 1, y = -2, z = 3
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document.write( "                  -2(1)+3(-2)+5(3)= 7
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document.write( "                       -2 -6 + 15 = 7
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document.write( "                                7 = 7 ----------> True\r
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document.write( "Therefore, the solution is x = 1, y = -2 and z = 3\r
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