document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98330>Question 98330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the question below.<BR>\n" );
document.write( "Find the values of the constants a and b if<BR>\n" );
document.write( "3x+5=a(x-1)+b(2x+3),     for all x£R </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71518 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=71518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the values of the constants a and b if<BR>\n" );
document.write( "3x+5=a(x-1)+b(2x+3), for all x£R<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "3x+5 = ax-a+2bx+3b<BR>\n" );
document.write( "3x+5 = (a+2b)x+(-a+3b)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Equating the corresponding coefficients you get:<BR>\n" );
document.write( "a+2b=3<BR>\n" );
document.write( "-a+3b=5<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Add the two equations to get:<BR>\n" );
document.write( "5b=8<BR>\n" );
document.write( "b=8/5<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Subtitute into a+2b=3 to solve for \"a\":<BR>\n" );
document.write( "a+2(8/5)=3<BR>\n" );
document.write( "a+16/5 = 15/5<BR>\n" );
document.write( "a = -1/5<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Check the answer in -a+3b=5<BR>\n" );
document.write( "1/5 + 3(8/5) = 5<BR>\n" );
document.write( "1/5 +24/5 = 5<BR>\n" );
document.write( "5=5<BR>\n" );
document.write( "========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );