document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=598657>Question 598657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> :( I need help desperately, I was absent throughout this entire section :( <BR>\n" );
document.write( "please help. i'm crying , i cant do it all\r<BR>\n" );
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document.write( "This is Solving substitution by elimination.\r<BR>\n" );
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document.write( "4) <BR>\n" );
document.write( "-5x+2y=-2<BR>\n" );
document.write( "-7x-2y=-24\r<BR>\n" );
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document.write( "5)<BR>\n" );
document.write( "-2x-y=-3<BR>\n" );
document.write( "5x+y=12\r<BR>\n" );
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document.write( "-\r<BR>\n" );
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document.write( "12)<BR>\n" );
document.write( "y=-4x-10<BR>\n" );
document.write( "y=-7x+12\r<BR>\n" );
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document.write( "13)<BR>\n" );
document.write( "y=3x+14<BR>\n" );
document.write( "y=-2x+4\r<BR>\n" );
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document.write( "14)<BR>\n" );
document.write( "y=2x-1<BR>\n" );
document.write( "2x-7y=-17\r<BR>\n" );
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document.write( "15)<BR>\n" );
document.write( "y=-3x-6<BR>\n" );
document.write( "7x+3y=-14\r<BR>\n" );
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document.write( "16)<BR>\n" );
document.write( "3x+y=-2<BR>\n" );
document.write( "-6x-y=2\r<BR>\n" );
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document.write( "17)<BR>\n" );
document.write( "6x-2y=-24<BR>\n" );
document.write( "7x+y=-18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378664 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there (again)--<BR>\n" );
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document.write( "The elimination method of solving systems of equations is also called the addition method. Let's solve the following system using addition/elimination.<BR>\n" );
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document.write( "-5x + 2y = - 2<BR>\n" );
document.write( "-7x - 2y = -24<BR>\n" );
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document.write( "Note that, if we add down, the y-terms will cancel out because 2y +(-2y) = 0. We'll draw an \"equals\" bar under the system, and add down. (We are adding like terms together.)<BR>\n" );
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document.write( "-5x + 2y = - 2<BR>\n" );
document.write( "-7x - 2y = -24<BR>\n" );
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document.write( "-12x     = -26<BR>\n" );
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document.write( "We have eliminated the y-term. Now we can divide both sides of the new equation by -12 to solve for x. <BR>\n" );
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document.write( "x = (-26)/(-12)<BR>\n" );
document.write( "x = 13/6<BR>\n" );
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document.write( "We want to know what the y-value is when x=13/6, so we substitute 13/6 for y in one of the original equations. It doesn't matter which one we choose. Let's use the first equation since the numbers are a little smaller.<BR>\n" );
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document.write( "-5x + 2y = - 2<BR>\n" );
document.write( "-5*(13/6) + 2y = -2<BR>\n" );
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document.write( "Now we'll simplify the equation and solve for y.<BR>\n" );
document.write( "-65/6 + 2y = -2<BR>\n" );
document.write( "2y = -2 + 65/6<BR>\n" );
document.write( "2y = -12/6 + 65/6<BR>\n" );
document.write( "2y = 53/6<BR>\n" );
document.write( "y = (53/6) / 2<BR>\n" );
document.write( "y = 53/12<BR>\n" );
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document.write( "Using the elimination method we find that the ordered pair (x,y)=(13/6, 53/12) is the solution for this system.<BR>\n" );
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document.write( "You should ALWAYS check your solution in both equations because it's quite easy to make an arithmetic error when using the elimination method.<BR>\n" );
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document.write( "FIRST EQUATION:<BR>\n" );
document.write( "-5x + 2y = - 2<BR>\n" );
document.write( "-5*(13/6) + 2*(53/12) = -2<BR>\n" );
document.write( "-65/6 + 106/12 = -2<BR>\n" );
document.write( "-130/12 + 106/12 = -2<BR>\n" );
document.write( "-24/12 = -2<BR>\n" );
document.write( "-2 = -2<BR>\n" );
document.write( "Check!<BR>\n" );
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document.write( "SECOND EQUATION<BR>\n" );
document.write( "-7x - 2y = -24<BR>\n" );
document.write( "-7(13/6) - 2(53/12) = -24<BR>\n" );
document.write( "-91/6 - 106/12 = -24<BR>\n" );
document.write( "-182/12 - 106/12 = -24<BR>\n" );
document.write( "-288/12 = -24<BR>\n" );
document.write( "-24 = -24<BR>\n" );
document.write( "Check!<BR>\n" );
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document.write( "Know we know for sure that the ordered pair (x,y)=(13/6, 53/12) is the solution for this system.<BR>\n" );
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document.write( "This was the simplest case of the elimination method because we add like terms in each equation with opposite signs [2y and -2y). <BR>\n" );
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document.write( "Make sure you understand this solution now. Then try problem #5 yourself. It's very similar.<BR>\n" );
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document.write( "As you post on algebra.com in the future, I suggest you post one, or perhaps two. problems at a time. Most tutors will provide more explanation if you do that.<BR>\n" );
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document.write( "Good luck,<BR>\n" );
document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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