document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346901>Question 346901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving the following using the substitution method and the elimination method.  I am so stuck trying to figure these out.\r<BR>\n" );
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document.write( "4x+3y=48<BR>\n" );
document.write( "3x+2y=34 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248120 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=248120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the following using the substitution method and the elimination method.<BR>\n" );
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document.write( "4x+3y=48<BR>\n" );
document.write( "3x+2y=34<BR>\n" );
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document.write( "Use the 2nd equation for substitution<BR>\n" );
document.write( "3x + 2y = 34<BR>\n" );
document.write( "2y = -3x + 34<BR>\n" );
document.write( "Divide both sides by 2<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34%2F2 ALIGN=MIDDLE  ALT=\"34%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = -1.5x + 17<BR>\n" );
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document.write( "Substitute (-1.5x+17) for y in the 1st equation <BR>\n" );
document.write( "4x + 3(-1.5x + 17) = 48<BR>\n" );
document.write( "4x - 4.5x + 51 = 48<BR>\n" );
document.write( "4x - 4.5y = 48 - 51<BR>\n" );
document.write( "-.5x = -3<BR>\n" );
document.write( "x has to be positive, multiply both sides by -1<BR>\n" );
document.write( ".5x = 3<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F.5 ALIGN=MIDDLE  ALT=\"3%2F.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "find y using y = -1.5x+17<BR>\n" );
document.write( "y = -1.5(6) + 17<BR>\n" );
document.write( "y = -9 + 17<BR>\n" );
document.write( "y = +8<BR>\n" );
document.write( "Check solutions in the 2nd equation; 3x+2y=34<BR>\n" );
document.write( "3(6) + 2(8) = 34<BR>\n" );
document.write( "18 + 16 = 34<BR>\n" );
document.write( "34 = 34; confirms our solutions<BR>\n" );
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document.write( "By elimination<BR>\n" );
document.write( "4x+3y=48<BR>\n" );
document.write( "3x+2y=34<BR>\n" );
document.write( "Multiply the 1st equation by 2, and the 2nd equation by 3<BR>\n" );
document.write( "8x + 6y = 96<BR>\n" );
document.write( "9x + 6y = 102<BR>\n" );
document.write( "------------------subtraction eliminates y, find x<BR>\n" );
document.write( "-1x = -6<BR>\n" );
document.write( "x = 6; mult by -1<BR>\n" );
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document.write( "You can find y using either equation, replacing x with 6 </SPAN>\n" );
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