document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70664>Question 70664</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0028253272/algebrahomeworkh>glencoe</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 3y-x=2<BR>\n" );
document.write( "-2y-x=-18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50454 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=50454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> +3y - x =   2<BR>\n" );
document.write( "-2y - x = -18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "One of the ways to solve this system of equations is to eliminate one of the variables<BR>\n" );
document.write( "and solve the resulting equation for the other variable.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In the above problem you can notice that there is a -x in the top equation and a -x in the<BR>\n" );
document.write( "bottom equation.  If you subtract the bottom equation from the top equation, the equation<BR>\n" );
document.write( "that results does not contain an x.  Remember the algebraic rule for subtracting ... change<BR>\n" );
document.write( "the signs of the subtrahend (number being subtracted) and add the result to the number that <BR>\n" );
document.write( "the subtrahend is being subtracted from.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "To follow this rule we change the sign of -2y so that it becomes +2y.  We also change the <BR>\n" );
document.write( "sign of the -x so that it becomes +x. And finally, we change the sign of the -18 to +18.  <BR>\n" );
document.write( "Then we add these terms to the terms directly above them.  In algebrais form this becomes: <BR>\n" );
document.write( ".<BR>\n" );
document.write( "+3y - x =  +2<BR>\n" );
document.write( "+2y + x = +18<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "+5y     = +20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The expression below the dashed line is a new equation resulting from the addition.<BR>\n" );
document.write( "You can solve this new equation for y by dividing both sides by 5 to get y = 4.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next take that value for y and plug it into either of the original two equations and solve<BR>\n" );
document.write( "for x.  For example, if we substitute 4 for y in the equation 3y - x = 2, we get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3*4 - x = 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "12 - x = 2<BR>\n" );
document.write( ". <BR>\n" );
document.write( "Subtracting 12 from both sides results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-x = -10<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And finally, we need to solve for +x, so multiply both sides of the equation by -1 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x = 10<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The answers you are looking for are x = 10 and y = 4.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you understand one method of solving a system of two linear equations.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );