document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21018>Question 21018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in class we're learning about system of equations and i don't really understand it so what is the coordinate for x-4y=15 and 2x+5y=4. could you explain it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10080 by </B><A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><B>mmm4444bot(95)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><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=10080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello There:\r<BR>\n" );
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document.write( "Off the top of my head, I can think of five different ways to solve this problem.  I don't know which method(s) you've studied, so I have to guess.\r<BR>\n" );
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document.write( "I'll use the \"substitution method\".\r<BR>\n" );
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document.write( "The strategy in this method is to solve one of the equations for one of the variables.  You'll end up with an expression that contains the other variable.\r<BR>\n" );
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document.write( "Substitute this expression into the other equation, and that will give you an equation that contains only one variable.  Solve it in the normal way.\r<BR>\n" );
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document.write( "Once you have the value of that variable, substitute it into the expression you got from solving the first equation.\r<BR>\n" );
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document.write( "Here goes:\r<BR>\n" );
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document.write( "I choose to solve the first equation for 'y'.\r<BR>\n" );
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document.write( "x - 4*y = 15\r<BR>\n" );
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document.write( "-4*y = 15 - x\r<BR>\n" );
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document.write( "y = (15 - x)/(-4)\r<BR>\n" );
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document.write( "Now I substitute this expression for y in the second equation.\r<BR>\n" );
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document.write( "2*x + 5*y = 4\r<BR>\n" );
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document.write( "2*x + 5 = 4\r<BR>\n" );
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document.write( "I'll clear the fraction by multiplying both sides by -4.\r<BR>\n" );
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document.write( "-8*x + 5*(15 - x) = -16\r<BR>\n" );
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document.write( "-8*x + 75 - 5*x = -16\r<BR>\n" );
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document.write( "-13*x = -91\r<BR>\n" );
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document.write( "x = -91/(-13)\r<BR>\n" );
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document.write( "x = 7\r<BR>\n" );
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document.write( "Now that we know x is 7, we substitute it for x in our formula for y above.\r<BR>\n" );
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document.write( "y = (15 - x)/(-4)\r<BR>\n" );
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document.write( "y = (15 - 7)/(-4)\r<BR>\n" );
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document.write( "y = 8/(-4)\r<BR>\n" );
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document.write( "y = -2\r<BR>\n" );
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document.write( "The solution is x = 7 and y = -2.\r<BR>\n" );
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document.write( "You can verify this solution by substituting 7 for x and -2 for y into both of the original equations to see that it yields true statements.\r<BR>\n" );
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document.write( "~ Mark<BR>\n" );
document.write( " </SPAN>\n" );
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