document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113239>Question 113239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x + y = 2 and 2x-y=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82407 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=82407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the two equations:<BR>\n" );
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document.write( "3x + y = 2<BR>\n" );
document.write( "2x - y = 3<BR>\n" );
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document.write( "This pair of equations is \"nicely\" arranged for solving by variable elimination because<BR>\n" );
document.write( "one of the terms in the top equation [that term is +y] is equal but with the opposite<BR>\n" );
document.write( "sign to the corresponding term in the bottom equation [that term is -y]. If you add these<BR>\n" );
document.write( "two equations vertically, the y-column will disappear because +y added to -y cancels<BR>\n" );
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document.write( "In the x column the 3x adds to the 2x and equals 5x. As we mentioned, in the y column the<BR>\n" );
document.write( "+y and the -y sum to zero and therefore are gone. And on the other side of the equal sign<BR>\n" );
document.write( "the +2 and the +3 add to 5. So, after adding the two equations vertically you are left<BR>\n" );
document.write( "with 5x = 5. You can solve this equation for x by dividing both sides of this equation by<BR>\n" );
document.write( "5 (the multiplier of the x) and you get:<BR>\n" );
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document.write( "x = 5/5 = 1<BR>\n" );
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document.write( "So you now know that x = 1<BR>\n" );
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document.write( "You can then go back to either one of the two equations you were given and replace x by 1<BR>\n" );
document.write( "in that equation and then solve for y. Let's go back to the first equation:<BR>\n" );
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document.write( "3x + y = 2<BR>\n" );
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document.write( "replace x by 1 and the equation becomes:<BR>\n" );
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document.write( "3(1) + y = 2<BR>\n" );
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document.write( "do the multiplication of 3 times 1 and the equation reduces to:<BR>\n" );
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document.write( "3 + y = 2<BR>\n" );
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document.write( "Get rid of the 3 on the left side by subtracting 3 from both sides of the equation to<BR>\n" );
document.write( "reach the solution:<BR>\n" );
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document.write( "y = 2 - 3 = -1<BR>\n" );
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document.write( "So the solution to this problem is x = 1 and y = -1<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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document.write( " </SPAN>\n" );
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