document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476503>Question 476503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x+3y=8<BR>\n" );
document.write( "3x+2y=7<BR>\n" );
document.write( "I have to determind how many solutions exit.<BR>\n" );
document.write( "Use either elimination or substitution to find solutions.\r<BR>\n" );
document.write( "\n" );
document.write( "I have tried and my teacher told me I had every question wrong. I am lost please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326704 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this problem I think elimination is the best way to find solution.<BR>\n" );
document.write( "Step 1: Determine which variable you want to eliminate<BR>\n" );
document.write( "Step 2: Find the least common multiple of the 2 coefficients.<BR>\n" );
document.write( "Step 3: Multiply each equation by appropriate scale factor such that the coefficients will be equal but have opposite signs.<BR>\n" );
document.write( "Step 4: Add the equations<BR>\n" );
document.write( "Step 5: Solve the resulting single-variable equation.<BR>\n" );
document.write( "Step 6: Substitute value back into one of the original equations to solve for 2nd variable. <BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y=8 ALIGN=MIDDLE  ALT=\"2x%2B3y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y=7 ALIGN=MIDDLE  ALT=\"3x%2B2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 1: Eliminate x<BR>\n" );
document.write( "Step 2: Least common multiple of 2 and 3 is 6.<BR>\n" );
document.write( "Best way to do this is multiply them together...2*3=6<BR>\n" );
document.write( "Step 3: Goal is to have 6x on top and -6x on bottom<BR>\n" );
document.write( "Multiply top equation by 3... 2x*3 = 6x<BR>\n" );
document.write( "Multiply bottom equation by -2... 3x*-2 = -6x<BR>\n" );
document.write( "Equations change to: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B+9y+=+24 ALIGN=MIDDLE  ALT=\"6x+%2B+9y+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x+-4y+=+-14 ALIGN=MIDDLE  ALT=\"-6x+-4y+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 4: Add equations, just add the coefficients in each column<BR>\n" );
document.write( "Result:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x+%2B5y+=+10 ALIGN=MIDDLE  ALT=\"0x+%2B5y+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 5: solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+10 ALIGN=MIDDLE  ALT=\"5y+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2 ALIGN=MIDDLE  ALT=\"y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 6: Pick 1 of the original equations and replace y with 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+3%282%29+=+8 ALIGN=MIDDLE  ALT=\"2x+%2B+3%282%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+6+=+8 ALIGN=MIDDLE  ALT=\"2x+%2B+6+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+2 ALIGN=MIDDLE  ALT=\"2x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then there is one unique solution of x =1 , y = 2.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );