document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132744>Question 1132744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number plus half of another number equals 6; twice the first number minus three times the second number<BR>\n" );
document.write( "equals 4. What are the numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749863 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Algebraically....<br><BR>\n" );
document.write( "x + (1/2)y = 6<BR>\n" );
document.write( "2x - 3y = 4<br><BR>\n" );
document.write( "Double the first equation and subtract the second equation from the resulting equation; that will eliminate x and let you solve for y.  Then substituting that value of y in either of the original equations lets you solve for x.<br><BR>\n" );
document.write( "You can solve this kind of problem, if the numbers are \"nice\", mentally, without the formal algebra.<br><BR>\n" );
document.write( "One of the given equations says one number plus half of another number is equal to 6.  Since the fraction makes the arithmetic a bit harder, double that piece of information to find that twice the first number plus the second number is 12.<br><BR>\n" );
document.write( "Then the two pieces of information both involve twice the first number, so comparing the two equations (that is, subtracting one equation from the other) lets you find the second number.<br><BR>\n" );
document.write( "Then of course use that second.number with either of the original pieces of information to find the first number.<br><BR>\n" );
document.write( "You will find the informal path to the answer is EXACTLY the same as the algebraic path, but without the need for pencil and paper.<BR>\n" );
document.write( " </SPAN>\n" );
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