document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103038>Question 103038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello out there,I need some help with some problems,the first one is,Use elimination to solve:3x-y=15 and 5x+y=9.The next one is,Use elimination to solve:3x-2y=6 and x-2y=-2.The next one is,Use elimination to solve:x/2+2y=9 and 2x-y=18.And the last one is,Use elimination to solve:4x-y=-3 and 5x+2y=-20.Thanks to whoever can help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75018 by </B><A HREF=/tutors/aboutme.mpl?userid=elima><B>elima(1433)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=elima><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=75018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solving by elimination, means you want to eliminate one of the variables.<BR>\n" );
document.write( "1)3x-y=15 and 5x+y=9<BR>\n" );
document.write( "We first set up the equations so they are being added together;<BR>\n" );
document.write( "3x-y=15<BR>\n" );
document.write( "5x+y=9<BR>\n" );
document.write( "_______<BR>\n" );
document.write( "8x=24<BR>\n" );
document.write( "x=3<BR>\n" );
document.write( "Now we substitute 3 for x in either equation;<BR>\n" );
document.write( "5(3)+y=9<BR>\n" );
document.write( "15+y=9<BR>\n" );
document.write( "y=9-15<BR>\n" );
document.write( "y=-6\r<BR>\n" );
document.write( "\n" );
document.write( "2)3x-2y=6 and x-2y=-2<BR>\n" );
document.write( "3x-2y=6<BR>\n" );
document.write( "x-2y=-2<BR>\n" );
document.write( "________<BR>\n" );
document.write( "Since just by adding these two together will not eliminate a variable we need to multiply one of the equations by something that will make one of the variables cancel out. In this case lets multiply the second equation by -1;<BR>\n" );
document.write( "-1(x-2y=-2)<BR>\n" );
document.write( "-x+2y=2<BR>\n" );
document.write( "Now we can add them together canceling out one of the variables;<BR>\n" );
document.write( "3x-2y=6<BR>\n" );
document.write( "-x+2y=2<BR>\n" );
document.write( "_________<BR>\n" );
document.write( "2x=8<BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "x-2y=-2<BR>\n" );
document.write( "4-2y=-2<BR>\n" );
document.write( "-2y=-2-4<BR>\n" );
document.write( "-2y=-6<BR>\n" );
document.write( "y=3<BR>\n" );
document.write( "3)x/2+2y=9 and 2x-y=18<BR>\n" );
document.write( "Lets multiply the first equation by -4, so we can get rid of the fraction;<BR>\n" );
document.write( "-4(x/2+2y=9)<BR>\n" );
document.write( "-2x-8y=-36<BR>\n" );
document.write( "now lets add them together<BR>\n" );
document.write( "-2x-8y=-36<BR>\n" );
document.write( "2x-y=18<BR>\n" );
document.write( "________<BR>\n" );
document.write( "-9y=18<BR>\n" );
document.write( "y=-2<BR>\n" );
document.write( "2(-2)-y=18<BR>\n" );
document.write( "-4-y=18<BR>\n" );
document.write( "-y=14<BR>\n" );
document.write( "y=-14<BR>\n" );
document.write( "4)4x-y=-3 and 5x+2y=-20<BR>\n" );
document.write( "Multiply the first equation by 2;<BR>\n" );
document.write( "2(4x-y=-3)<BR>\n" );
document.write( "8x-2y=-6<BR>\n" );
document.write( "Now add;<BR>\n" );
document.write( "8x-2y=-6<BR>\n" );
document.write( "5x+2y=-20<BR>\n" );
document.write( "_________<BR>\n" );
document.write( "13x=-26<BR>\n" );
document.write( "x=-2<BR>\n" );
document.write( "4(-2)-y=-3<BR>\n" );
document.write( "-8-y=-3<BR>\n" );
document.write( "-y=-3+8<BR>\n" );
document.write( "-y=5<BR>\n" );
document.write( "y=-5<BR>\n" );
document.write( "Hope you got it all<BR>\n" );
document.write( ":) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );