document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73446>Question 73446</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1559533404/algebrahomeworkh>discovering algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How can we get an answer to Solving systems of equations using elimination, such as the one below\r<BR>\n" );
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document.write( "2x+5y=-1<BR>\n" );
document.write( "x+2y=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52580 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x+5y=-1<BR>\n" );
document.write( "x+ 2y= 0<BR>\n" );
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document.write( "The method to solve this equation set by elimination is to make a term in one of the equations<BR>\n" );
document.write( "equal to a term in the other equation and then subtract the two equations to get rid<BR>\n" );
document.write( "of the common term.<BR>\n" );
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document.write( "For this set of equations, the easiest thing to do would be to multiply the bottom equation<BR>\n" );
document.write( "by 2 (multiply all terms on both sides).  Then both of the equations would contain the<BR>\n" );
document.write( "term 2x and if you subtracted the two equations the result would be a single equation<BR>\n" );
document.write( "without any terms involving x.  This would be solvable.  But rather that do it the easy way,<BR>\n" );
document.write( "let's try to get rid of the y terms by making them equal in both equations.  This requires<BR>\n" );
document.write( "you to change both equations, not just one, and is more commonly what you might have to<BR>\n" );
document.write( "do.<BR>\n" );
document.write( "Again your two equations are:<BR>\n" );
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document.write( "2x+5y=-1<BR>\n" );
document.write( "x+ 2y= 0<BR>\n" );
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document.write( "To get rid of the y terms suppose we multiply the top equation by 2 (all terms on both<BR>\n" );
document.write( "sides). When we do it becomes:<BR>\n" );
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document.write( "4x + 10y = -2<BR>\n" );
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document.write( "Then suppose we multiply the bottom equation by 5 (same thing: multiply all terms on<BR>\n" );
document.write( "both sides). The result is:<BR>\n" );
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document.write( "5x + 10y = 0<BR>\n" );
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document.write( "So the set of equations we are dealing with has now been transformed to:<BR>\n" );
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document.write( "4x + 10y = -2<BR>\n" );
document.write( "5x + 10y = 0<BR>\n" );
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document.write( "If we now subtract these two, the terms in the y column will disappear.  In the x column<BR>\n" );
document.write( "we end up with -x and in the numbers column on the right side we end up with -2. So our<BR>\n" );
document.write( "new equation is:<BR>\n" );
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document.write( "-x = -2<BR>\n" );
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document.write( "and multiplying both sides by -1 gives us x = +2<BR>\n" );
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document.write( "We can now take that value back to any of the equations, substitute it, and solve for<BR>\n" );
document.write( "y.<BR>\n" );
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document.write( "Let's go back to the original bottom equation:<BR>\n" );
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document.write( "x + 2y = 0<BR>\n" );
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document.write( "Substitute +2 for x to get:<BR>\n" );
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document.write( "+2 + 2y = 0<BR>\n" );
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document.write( "Subtract 2 from both sides to eliminate the +2 on the left side and the equation becomes:<BR>\n" );
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document.write( "2y = -2<BR>\n" );
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document.write( "Finally divide both sides by 2 to find that y = -1<BR>\n" );
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document.write( "So the solution set for this pair of equations is x = 2 and y = -1 or in another way of<BR>\n" );
document.write( "looking at it, the graphs of the two equations intersect at the point (2, -1)<BR>\n" );
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document.write( "Hope this gives you a basic insight into solving two linear equations using the method<BR>\n" );
document.write( "of elimination. </SPAN>\n" );
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