document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64589>Question 64589</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937760/algebrahomeworkh>ALGEBRA 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve linear equations and inequalities of two variables?<BR>\n" );
document.write( "How do you graph linear equations of two variables? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46467 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> QUESTION:\r<BR>\n" );
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document.write( "A system of equations is a collection of two or more equations with the same set of unknowns. \r<BR>\n" );
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document.write( "ANSWER:\r<BR>\n" );
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document.write( "In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. \r<BR>\n" );
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document.write( "A system of linear equations can be solved four different ways: \r<BR>\n" );
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document.write( "Substitution,\r<BR>\n" );
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document.write( "Elimination,\r<BR>\n" );
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document.write( "Matrices,\r<BR>\n" );
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document.write( "Graphing. \r<BR>\n" );
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document.write( "___________________________________________________________________________\r<BR>\n" );
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document.write( "Let's discuss these methods with an example,\r<BR>\n" );
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document.write( "1.  Solve these equations.\r<BR>\n" );
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document.write( "x-y = 4____________________________(1)\r<BR>\n" );
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document.write( "3x + 2y = 7___________________________(2)\r<BR>\n" );
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document.write( "METHOD OF SUBSTITUTION:\r<BR>\n" );
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document.write( "(1)==> x = 4 + y ___________________________(3)\r<BR>\n" );
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document.write( "Substitute this value of x in (2)\r<BR>\n" );
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document.write( "==> 3(4+ y) + 2y = 7\r<BR>\n" );
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document.write( "==> 12 + 3y + 2y = 7\r<BR>\n" );
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document.write( "==> 12 + 5y = 7\r<BR>\n" );
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document.write( "==> 5y = 7 - 12\r<BR>\n" );
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document.write( "==> 5y = -5\r<BR>\n" );
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document.write( "==> y = -5/5\r<BR>\n" );
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document.write( "==> y = -1\r<BR>\n" );
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document.write( "Now put y = -1 in (3)\r<BR>\n" );
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document.write( "==> x = 4 + -1\r<BR>\n" );
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document.write( "==> x = 3\r<BR>\n" );
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document.write( "So Solution is x = 3 and y = -1\r<BR>\n" );
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document.write( "METHOD OF ELIMINATION:\r<BR>\n" );
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document.write( "x-y = 4____________________________(1)\r<BR>\n" );
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document.write( "3x + 2y = 7___________________________(2)\r<BR>\n" );
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document.write( "Multiply equation(1) by '2' so that  coefficient of y in both equations become same( but opposite sign).  Also we could make coefficient of x same.\r<BR>\n" );
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document.write( "==> 2x-2y = 8____________________________(3)\r<BR>\n" );
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document.write( "3x + 2y = 7___________________________(2)\r<BR>\n" );
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document.write( "Now add  (3) and (2)\r<BR>\n" );
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document.write( "==> 2x-2y + 3x + 2y = 8 + 7\r<BR>\n" );
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document.write( "==> 5x = 15\r<BR>\n" );
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document.write( "==> x = 15/5\r<BR>\n" );
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document.write( "==> x = 3\r<BR>\n" );
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document.write( "Now substitute value of x=3 in (1)\r<BR>\n" );
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document.write( "==> 3-y = 4\r<BR>\n" );
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document.write( "==> 3- 4 = y\r<BR>\n" );
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document.write( "==> -1 = y\r<BR>\n" );
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document.write( "That is  x= 3 and y = -1\r<BR>\n" );
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document.write( "______________________________________________________________________________\r<BR>\n" );
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document.write( "METHOD OG GRAPHING.\r<BR>\n" );
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document.write( "x-y = 4____________________________(1)\r<BR>\n" );
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document.write( "3x + 2y = 7___________________________(2)\r<BR>\n" );
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document.write( "First of all rewrite the equation in terms of 'x'\r<BR>\n" );
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document.write( "(1)==> y = x-4\r<BR>\n" );
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document.write( "Now give arbitrary values to 'x' like 0,1,2,3,...-1, -2,....(atleast 5 values)\r<BR>\n" );
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document.write( "and find out corresponding values of y.\r<BR>\n" );
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document.write( "for example, if we put x = 0, y = 0-4 = -4\r<BR>\n" );
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document.write( "if x = 1, y = 1-4= -3......and so on\r<BR>\n" );
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document.write( "Now plot these ordered pairs....\r<BR>\n" );
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document.write( "Similarly,\r<BR>\n" );
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document.write( "(2)==> 2y = 7 - 3x\r<BR>\n" );
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document.write( "==> y = 7/2 - (3/2)x\r<BR>\n" );
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document.write( "Here also give values to x and find out corresponding values of y and then plot the graph.\r<BR>\n" );
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document.write( "The resulting graph will come like this,\r<BR>\n" );
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document.write( "We can see that  two straight lines intersect at a single point.\r<BR>\n" );
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document.write( "Find out the coordinates of this point.\r<BR>\n" );
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document.write( "For that draw lines perpendicular to x axis and Y axis.\r<BR>\n" );
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document.write( "The perpendicular lines will meet the X axis at 3 and in the Y axis at -1\r<BR>\n" );
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document.write( "Which gives the soluton of these equations, that is,\r<BR>\n" );
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document.write( "x = 3 and y = -1\r<BR>\n" );
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document.write( "Hope you understood.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "Praseena.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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