document.write( "Question 995784: Solve the following system of equations using elimination or matrices.
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Algebra.Com's Answer #614505 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " x - 2y +  z =  6.   (1)\r\n" );
document.write( "2x +  y - 3z = -3,   (2)\r\n" );
document.write( " x - 3y + 3z = 10.   (3)\r\n" );
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document.write( "Let us apply the Gauss' elimination procedure. Multiply first eqn by 2 and then distract it from the second eqn. Then distract the first eqn from the third one. You will get\r\n" );
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document.write( " x - 2y +  z =  6.   (4)\r\n" );
document.write( "     5y - 5z = -15.  (5)\r\n" );
document.write( "    -y  + 2z =  4.   (6)\r\n" );
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document.write( "Thus you excluded x in the eqns (5) and (6). Next, in the eqn (5) divide both sides by 5. You will get\r\n" );
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document.write( " x - 2y +  z =  6.   (7)\r\n" );
document.write( "      y -  z = -3 .  (8)\r\n" );
document.write( "     -y + 2z =  4.   (9)\r\n" );
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document.write( "Now, add equations (8) and (9). You will get\r\n" );
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document.write( " x - 2y +  z =  6.   (10)\r\n" );
document.write( "      y -  z = -3 .  (11)\r\n" );
document.write( "           z =  1.   (12)\r\n" );
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document.write( "So, you just found the solution z = 1. Now, make back substitution in equations (11) and (10) and find y and then x.\r\n" );
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