document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23848>Question 23848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plaease help me use the substitution method to solve the linear system. \r<BR>\n" );
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document.write( "      y = x-4 <BR>\n" );
document.write( "      4x+y = 26 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12583 by </B><A HREF=/tutors/aboutme.mpl?userid=ilana><B>ilana(307)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ilana><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=12583\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By \"substitution,\" we mean starting with 2 equations and 2 variables, and replacing one variable to end up with 1 equation and 1 variable, which we then solve.<BR>\n" );
document.write( "Here, we have an equation of the form y=(something in terms of x), so it is simplest to substitute that equation for y in the other equation.<BR>\n" );
document.write( "So, we take x-4 for y and use that in the equation 4x+y=26, giving us 4x+(x-4)=26.<BR>\n" );
document.write( "We then simplify this to get 4x+x-4=26, so 5x-4=26, so 5x=30, and finally x=6.<BR>\n" );
document.write( "We then need only the value of y, so we use x=6 and y=x-4 to get y=(6)-4=2.<BR>\n" );
document.write( "So x=6 and y=2.\r<BR>\n" );
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document.write( "We can check these values in both equations and they should make the statements true:<BR>\n" );
document.write( "y=x-4: 2=6-4=2, so this is true.<BR>\n" );
document.write( "4x+y=26: 4(6)+(2) = 26<BR>\n" );
document.write( "         24+2=26  = 26, so this is true as well. </SPAN>\n" );
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