document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239735>Question 239735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: 5x-6x=-17 3x-4y+5z=-1 2z=-6. This is one problem or equation. Thank you I appreciate if you can help me understand the process involved with solving this type of equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175889 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x - 6x = -17<BR>\n" );
document.write( "3x - 4y + 5z = -1<BR>\n" );
document.write( "2z = -6\r<BR>\n" );
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document.write( "looks like you have 3 equations that have to be solved simultaneously.\r<BR>\n" );
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document.write( "looks like your third equation has already solved for z so we can start there.\r<BR>\n" );
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document.write( "2z = -6 becomes z = -3 when you divided both sides of the equation by 2.\r<BR>\n" );
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document.write( "z = -3 is the value of one of your variables.\r<BR>\n" );
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document.write( "you are left with:\r<BR>\n" );
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document.write( "5x - 6x = -17<BR>\n" );
document.write( "3x - 4y + 5z = -1\r<BR>\n" );
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document.write( "that first equation looks like it's all in x so we can solve for x from that equation.\r<BR>\n" );
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document.write( "5x - 6x = -17 becomes -x = -17 after you combine like terms.\r<BR>\n" );
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document.write( "multiply both sides of this equation by -1 to get:\r<BR>\n" );
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document.write( "x = 17\r<BR>\n" );
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document.write( "you now have two values out of the 3.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 17<BR>\n" );
document.write( "z = -3\r<BR>\n" );
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document.write( "you have only one equation left to solve.\r<BR>\n" );
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document.write( "that is:\r<BR>\n" );
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document.write( "3x - 4y + 5z = -1\r<BR>\n" );
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document.write( "replace x with 17 and z with -3 in that equation to get:\r<BR>\n" );
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document.write( "3*(17) - 4*y + 5*(-3) = -1\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "51 - 4*y - 15 = -1\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "36 - 4*y = -1\r<BR>\n" );
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document.write( "add 4*y to both sides of the equation and add 1 to both sides of the equation to get:\r<BR>\n" );
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document.write( "36 + 1 = 4*y\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "37 = 4*y\r<BR>\n" );
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document.write( "divide both sides of the equation by 4 to get:\r<BR>\n" );
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document.write( "9.25 = y\r<BR>\n" );
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document.write( "this is the same as:\r<BR>\n" );
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document.write( "y = 9.25\r<BR>\n" );
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document.write( "the answer to your equation is:\r<BR>\n" );
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document.write( "x = 17<BR>\n" );
document.write( "y = 9.25<BR>\n" );
document.write( "z = -3\r<BR>\n" );
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document.write( "substitute in your original equations to confirm these answers are good.\r<BR>\n" );
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document.write( "5x - 6x = -17<BR>\n" );
document.write( "3x - 4y + 5z = -1<BR>\n" );
document.write( "2z = -6\r<BR>\n" );
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document.write( "these become:\r<BR>\n" );
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document.write( "5*(17) - 6*(17) = -17<BR>\n" );
document.write( "3*(17) - 4*(9.25) + 5*(-3) = -1<BR>\n" );
document.write( "2*(-3) = -6\r<BR>\n" );
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document.write( "simplify and combine like terms to get:\r<BR>\n" );
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document.write( "-17 = -17<BR>\n" );
document.write( "51 - 37 - 15 = -1<BR>\n" );
document.write( "-6 = -6\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "-17 = -17<BR>\n" );
document.write( "-1 = -1<BR>\n" );
document.write( "-6 = -6\r<BR>\n" );
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document.write( "all equations confirm so the answer is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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