document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120131>Question 120131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7x-y=10<BR>\n" );
document.write( "x=2y-6\r<BR>\n" );
document.write( "\n" );
document.write( "I have to solve this problem using substitution and I don't understand and I'm really confused could someone please help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88041 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=88041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solv by the substitution method:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-y+=+10 ALIGN=MIDDLE  ALT=\"7x-y+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2y-6 ALIGN=MIDDLE  ALT=\"x+=+2y-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The idea behind the subtitution method of solving systems of equations, such as you have here, is to eliminate one of the two variables (x or y) so that you will have one equation with one unknown.<BR>\n" );
document.write( "Notice that equation 2) is conveniently written in terms of the variable x, that is, you have the variable x isolated on the left side while everything else is on the right side. This means that you can substitute the x in equation 1) with the x = 2y-6 of equation 2), then you will have equation 1) with only one variable (y) in it.<BR>\n" );
document.write( "1a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%282y-6%29-y+=+10 ALIGN=MIDDLE  ALT=\"7%282y-6%29-y+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814y-42%29-y+=+10 ALIGN=MIDDLE  ALT=\"%2814y-42%29-y+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like-terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13y-42+=+10 ALIGN=MIDDLE  ALT=\"13y-42+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 42 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13y+=+52 ALIGN=MIDDLE  ALT=\"13y+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 13.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4 ALIGN=MIDDLE  ALT=\"y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now you can substitute this value of y into either one of the two original equations to solve for the other variable, x. Let's use equation 2) for this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2y+-+6 ALIGN=MIDDLE  ALT=\"x+=+2y+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute y = 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%284%29-6 ALIGN=MIDDLE  ALT=\"x+=+2%284%29-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8-6 ALIGN=MIDDLE  ALT=\"x+=+8-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the solution is: (2, 4)<BR>\n" );
document.write( "Remember that the solution to a system two linear equations is the point of intersection of the two lines represented by the two equations,, if there is one.<BR>\n" );
document.write( "Let's look at the graph of the two equations and you'll see what I mean:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C400%2C-5%2C5%2C-5%2C5%2C7x-10%2C%281%2F2%29x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C400%2C-5%2C5%2C-5%2C5%2C7x-10%2C%281%2F2%29x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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