document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572581>Question 572581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve by the substitution method<BR>\n" );
document.write( "4x-4y=0<BR>\n" );
document.write( "7x+54=y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368589 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you solve by substitution, you're looking for one of the variables to be alone on one side of one of the equations.  In this case, you have Y by itself in the 2nd equation.  What we do then is \"substitute\" for Y in the first equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, <BR>\n" );
document.write( "4X - 4Y = 0<BR>\n" );
document.write( "But we know from the 2nd equation that Y is 7X+54<BR>\n" );
document.write( "So every time they use Y in the first equation, substitute this instead.<BR>\n" );
document.write( "4X - 4Y = 0<BR>\n" );
document.write( "4X - 4(7X+54) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiplying to get rid of the parens:<BR>\n" );
document.write( "4X - 28X - 216 = 0<BR>\n" );
document.write( "-24X - 216 = 0<BR>\n" );
document.write( "Add 24X to both sides:<BR>\n" );
document.write( "-216 = 24X<BR>\n" );
document.write( "Divide both sides by 24:<BR>\n" );
document.write( "-9 = X\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But we still need Y:<BR>\n" );
document.write( "7X+54 = Y<BR>\n" );
document.write( "7(-9)+54 = Y<BR>\n" );
document.write( "-63+54=Y<BR>\n" );
document.write( "-9=Y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Checking:<BR>\n" );
document.write( "4(-9)-4(-9) = 0<BR>\n" );
document.write( "-36 + 36 = 0 Correct<BR>\n" );
document.write( "Next equation:<BR>\n" );
document.write( "7(-9) + 54 = -9<BR>\n" );
document.write( "-63 + 54=-9<BR>\n" );
document.write( "-9 = -9   Correct! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );