document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254478>Question 254478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the substitution method to solve the linear system given. Express<BR>\n" );
document.write( "    the answer as an ordered pair of the form (x,y)<BR>\n" );
document.write( "     x + y = 5<BR>\n" );
document.write( "    2x + y = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186819 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=186819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   x + y = 5<BR>\n" );
document.write( " 2x + y = 6\r<BR>\n" );
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document.write( "What if you took the first equation and solved for \"X\".  Let's do that.  Let's take the first equation and solve for \"X\".\r<BR>\n" );
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document.write( "x + y = 5(first equation)<BR>\n" );
document.write( "x     = 5 - y (subtract y from both sides to isolate/solve for \"X\")\r<BR>\n" );
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document.write( "Now that you know x = 5 - y, you can SUBSTITUTE 5 - y into the 2nd equation, where the \"X\" variable is.\r<BR>\n" );
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document.write( " 2x + y = 6  (2nd original equation)<BR>\n" );
document.write( "2(5 - y) + y = 6 (see where \"X\" was replaced with 5 - y)?<BR>\n" );
document.write( "10 - 2y + y = 6 (distribute the 2 and multiply 2 times 5 and then 2 times -y)<BR>\n" );
document.write( "10 - 1y = 6 (combine like terms:  -2y + y = -1y)<BR>\n" );
document.write( "-1y = 6 - 10 (subtract 10 from both sides to isolate the \"Y\")<BR>\n" );
document.write( "-1y = -4 (6 - 10 = -4)<BR>\n" );
document.write( "y = 4 (divide both sides by -1 to isolate the y).\r<BR>\n" );
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document.write( "Now you know that y = 4.   Let's put that info into our first equation:\r<BR>\n" );
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document.write( " x + y = 5 (original equation)<BR>\n" );
document.write( "x + 4 = 5  (see where \"Y\" was replaced with the number 4)?<BR>\n" );
document.write( "x = 5 - 4 (subtract 4 on both sides to isolate the \"X\")<BR>\n" );
document.write( "x = 1   \r<BR>\n" );
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document.write( "Now you know that x = 1.   \r<BR>\n" );
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document.write( "The ordered pair then, which is in this format (x, y) is (1, 4).\r<BR>\n" );
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document.write( "Does this work in the answer?  Let's \"plug\" in the x and y info into the original equations:\r<BR>\n" );
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document.write( "  x + y = 5  (first original equation)<BR>\n" );
document.write( "  1 + 4 = 5  (equation with x and y info \"plugged\" in)<BR>\n" );
document.write( "  5 = 5  YES the ordered pair (1, 4) fits in this equation and makes it true.\r<BR>\n" );
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document.write( " 2x + y = 6 (second original equation)<BR>\n" );
document.write( " 2(1) + 4 = 6 (equation with x and y info \"plugged\" in)<BR>\n" );
document.write( "2 + 4 = 6<BR>\n" );
document.write( "6 = 6 YES the ordered pair (1,4) fits into this equation as well and makes it true. \r<BR>\n" );
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document.write( "I hope this is helpful to you. :-) </SPAN>\n" );
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