document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173015>Question 173015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is how to do substitution. I am extremely confused because with it because my teacher will not explain it well no matter what.<BR>\n" );
document.write( "As an example, questions like these:<BR>\n" );
document.write( "y=5-4*x<BR>\n" );
document.write( "3*x-2*y=12<BR>\n" );
document.write( "Please help and possibly explain in detail how to solve these problems.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127887 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=127887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=5-4*x<BR>\n" );
document.write( "3*x-2*y=12<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can write it like this<BR>\n" );
document.write( "y = 5 - 4x<BR>\n" );
document.write( "3x - 2y = 12<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Look at the 1st equation; that means that any place you see y, you can substitute<BR>\n" );
document.write( "(5-4x) for it<BR>\n" );
document.write( ":<BR>\n" );
document.write( "In the 2nd equation (3x - 2y = 12), we can substitute (5-4x) for y, so we have<BR>\n" );
document.write( "3x - 2(5-4x) = 12<BR>\n" );
document.write( "That gives just one unknown (x), which is easy to solve with basic algebra:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply what's inside the brackets by -2 and you have:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3x - 10 + 8x = 12; note that a minus times a minus is plus<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Perform the necessary operations to get the variables on the left, numbers on the right<BR>\n" );
document.write( "3x + 8x = 12 + 10; added 10 to both sides<BR>\n" );
document.write( ":<BR>\n" );
document.write( "11x = 22<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2F11 ALIGN=MIDDLE  ALT=\"22%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >; divided both sides by 11<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Now substitute 2 for x in the 1st original equation and find y:<BR>\n" );
document.write( "y = 5 - 4x<BR>\n" );
document.write( "y = 5 - 4(2)<BR>\n" );
document.write( "y = 5 - 8<BR>\n" );
document.write( "y = -3<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check by substituting both solution for x and y in the 2nd equation<BR>\n" );
document.write( "3x - 2y = 12<BR>\n" );
document.write( "3(2) - 2(-3) = 12<BR>\n" );
document.write( "6 + 6 = 12; which is true.  (remember minus times a minus is a plus)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "How about this, did it make sense to you, now? </SPAN>\n" );
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