document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085986>Question 1085986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve by comparison<BR>\n" );
document.write( " x+2y =4<BR>\n" );
document.write( "x+y=2\r<BR>\n" );
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document.write( "another<BR>\n" );
document.write( "x-4y=1<BR>\n" );
document.write( "x+y=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700099 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the comparison method essentially solves each equation for a selected variable and then compares the value of that same variable to each other.\r<BR>\n" );
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document.write( "the concept uses the basic mathematical rule of:\r<BR>\n" );
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document.write( "if a = b and a = c, then b = c because they are both equal to a.\r<BR>\n" );
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document.write( "note that, if you subtract the second equation from the first, you will get:\r<BR>\n" );
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document.write( "a = b minus a = c becomes 0 = b - c<BR>\n" );
document.write( "add c to both sides of this equation to get c = b which is the same as b = c.\r<BR>\n" );
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document.write( "using this concept, you would do the following:\r<BR>\n" );
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document.write( "for the first set of equations:\r<BR>\n" );
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document.write( "x+2y = 4<BR>\n" );
document.write( "x+y=2 \r<BR>\n" );
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document.write( "solve for x in both equations.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "x = 4 - 2y<BR>\n" );
document.write( "x = 2 - y\r<BR>\n" );
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document.write( "since both expressions on the right are equal to x, then set them equal to each other and solve.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "4 - 2y = 2 - y\r<BR>\n" );
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document.write( "add 2y to both sides of the equation and subtract 2 from both sides of the equation to get:\r<BR>\n" );
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document.write( "4 - 2 = -y + 2y\r<BR>\n" );
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document.write( "combine like terms to get 2 = y\r<BR>\n" );
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document.write( "use the value of 2 for y in either original equation to find x.\r<BR>\n" );
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document.write( "x+y=2 becomes x + 2 = 2 which becomes x = 0.\r<BR>\n" );
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document.write( "your values are x = 0 and y = 2.\r<BR>\n" );
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document.write( "both original equations will be true with these value as shown below:\r<BR>\n" );
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document.write( "x+2y = 4 becomes 0 + 2*2 = 4 which becomes 4 = 4 which is true.\r<BR>\n" );
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document.write( "x + y = 2 becomes 0 + 2 = 2 which becomes 2 = 2 which is true.\r<BR>\n" );
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document.write( "in the second set of equations, start with:\r<BR>\n" );
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document.write( "x-4y=1<BR>\n" );
document.write( "x+y=-4\r<BR>\n" );
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document.write( "solve for x in both equations to get:\r<BR>\n" );
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document.write( "x = 4y + 1<BR>\n" );
document.write( "x = -4 - y\r<BR>\n" );
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document.write( "since both expressions on the right side of the equal sign are both equal to x, set them equal to each other to get:\r<BR>\n" );
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document.write( "4y + 1 = -4 - y\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation and add y to both sides of the equation to get:\r<BR>\n" );
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document.write( "5y = -5\r<BR>\n" );
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document.write( "solve for y to get y = -5/5 = -1\r<BR>\n" );
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document.write( "replace y with -1 in either original equation to find the value of x.\r<BR>\n" );
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document.write( "x-4y=1 becomes x - 4*(-1) = 1 which becomes x + 4 = 1 which becomes x = -3\r<BR>\n" );
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document.write( "when x = -3 and y = -1, both original equations should be true.\r<BR>\n" );
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document.write( "x-4y=1 becomes -3 - 4 * -1) = 1 which becomes -3 + 4 = 1 which becomes 1 = 1 which it true.\r<BR>\n" );
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document.write( "x+y=-4 becomes -3 + (-1) = -4 which becomes -3 - 1 = -4 which becomes -4 = -4 which is true.\r<BR>\n" );
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document.write( "both original equations are true, so the solution is good.\r<BR>\n" );
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document.write( "here's a reference on the comparison method.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://study.com/academy/lesson/comparison-method-for-solving-math-problems.html\" target= \"_blank\">http://study.com/academy/lesson/comparison-method-for-solving-math-problems.html</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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