document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151845>Question 1151845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x + y = 5<BR>\n" );
document.write( "−x − 2y + 8z = 8<BR>\n" );
document.write( "−y + 4z = 6<BR>\n" );
document.write( "This is my first question! find, x,y,z and make sure that they are all true! \r<BR>\n" );
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document.write( "3x + 4y + z = 15<BR>\n" );
document.write( "x − 2y + z = −15<BR>\n" );
document.write( "2x + y + z = 5<BR>\n" );
document.write( "This is my second question! find, x,y,z and make sure that they are all true! \r<BR>\n" );
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document.write( "thank you to whoever answers this correctly! thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773723 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=773723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll get you started on each problem. \r<BR>\n" );
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document.write( "================================================================\r<BR>\n" );
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document.write( "Problem 1\r<BR>\n" );
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document.write( "2x+y = 5 ............ equation (1)\r\n" );
document.write( "-x - 2y + 8z = 8 .... equation (2)\r\n" );
document.write( "-y + 4z = 6 ......... equation (3)\r\n" );
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document.write( "Note how there's a 'y' term in the first equation that has a coefficient of 1. This allows us to easily solve for y without involving fractions.<BR>\n" );
document.write( "2x+y = 5<BR>\n" );
document.write( "2x+y-2x = 5-2x<BR>\n" );
document.write( "y = -2x+5\r<BR>\n" );
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document.write( "This can be plugged into the other equations to get rid one of the variables\r<BR>\n" );
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document.write( "Let's plug it into equation (2)<BR>\n" );
document.write( "-x - 2y + 8z = 8<BR>\n" );
document.write( "-x - 2( y ) + 8z = 8<BR>\n" );
document.write( "-x - 2( -2x+5 ) + 8z = 8 .... replace y with -2x+5, y is eliminated temporarily<BR>\n" );
document.write( "-x + 4x - 10 + 8z = 8<BR>\n" );
document.write( "3x - 10 + 8z = 8<BR>\n" );
document.write( "3x - 10 + 8z + 10 = 8 + 10 ... add 10 to both sides<BR>\n" );
document.write( "3x + 8z = 18 .... Call this equation (4)\r<BR>\n" );
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document.write( "Plug y = -2x+5 into equation (3) now<BR>\n" );
document.write( "-y + 4z = 6<BR>\n" );
document.write( "-( y ) + 4z = 6<BR>\n" );
document.write( "-( -2x+5 ) + 4z = 6<BR>\n" );
document.write( "2x - 5 + 4z = 6<BR>\n" );
document.write( "2x - 5 + 4z+5 = 6+5 ... add 5 to both sides<BR>\n" );
document.write( "2x + 4z = 11 .... Call this equation (5)\r<BR>\n" );
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document.write( "The system of equations we were given reduces to this<BR>\n" );
document.write( "3x + 8z = 18 .... Equation (4)<BR>\n" );
document.write( "2x + 4z = 11 .... Equation (5)\r<BR>\n" );
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document.write( "I'll let you take over from here.\r<BR>\n" );
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document.write( "================================================================\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "3x + 4y + z = 15 .... equation (1)\r\n" );
document.write( "x - 2y + z = -15 .... equation (2)\r\n" );
document.write( "2x + y + z = 5 ...... equation (3)\r\n" );
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document.write( "Solve equation (1) for z<BR>\n" );
document.write( "3x + 4y + z = 15<BR>\n" );
document.write( "3x + 4y + z-3x = 15-3x .... subtract 3x from both sides<BR>\n" );
document.write( "4y+z = 15-3x<BR>\n" );
document.write( "4y+z-4y = 15-3x-4y .... subtract 4y from both sides<BR>\n" );
document.write( "z = -3x-4y+15\r<BR>\n" );
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document.write( "Move onto equation (2) and plug in z = -3x-4y+15<BR>\n" );
document.write( "x - 2y + z = -15<BR>\n" );
document.write( "x - 2y + ( z ) = -15<BR>\n" );
document.write( "x - 2y + ( -3x-4y+15 ) = -15 ... replace z with  -3x-4y+15<BR>\n" );
document.write( "x - 2y - 3x-4y+15 = -15<BR>\n" );
document.write( "-2x - 6y + 15 = -15<BR>\n" );
document.write( "-2x - 6y + 15-15 = -15-15<BR>\n" );
document.write( "-2x - 6y = -30 .... call this equation (4)\r<BR>\n" );
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document.write( "Do the same for equation (3)<BR>\n" );
document.write( "2x + y + z = 5<BR>\n" );
document.write( "2x + y + (z) = 5<BR>\n" );
document.write( "2x + y + (-3x-4y+15) = 5  ... replace z with  -3x-4y+15<BR>\n" );
document.write( "2x + y - 3x-4y+15 = 5<BR>\n" );
document.write( "-x -3y + 15 = 5<BR>\n" );
document.write( "-x -3y + 15-15 = 5-15<BR>\n" );
document.write( "-x -3y = -10 .... call this equation (5)\r<BR>\n" );
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document.write( "Equations (4) and (5) form a simpler system<BR>\n" );
document.write( "-2x - 6y = -30<BR>\n" );
document.write( "-x - 3y = -10\r<BR>\n" );
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document.write( "I'll let you solve this system. <BR>\n" );
document.write( "Once you know x and y, use those values to find z.\r<BR>\n" );
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