document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171380>Question 1171380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Have I correctly solved the 4 problems below using the systems of simultaneous equations, using either the substitution method or the addition method?\r<BR>\n" );
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document.write( "Problem 1\r<BR>\n" );
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document.write( "x+2y=15<BR>\n" );
document.write( "x-2y=-9\r<BR>\n" );
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document.write( "2x =6\r<BR>\n" );
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document.write( "x=3\r<BR>\n" );
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document.write( "3+2y=15<BR>\n" );
document.write( "2y=15-3<BR>\n" );
document.write( "2y=12\r<BR>\n" );
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document.write( "y=6\r<BR>\n" );
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document.write( "Problem 2:\r<BR>\n" );
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document.write( "x-y=0<BR>\n" );
document.write( "7x-3y=24\r<BR>\n" );
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document.write( "-3(x-y)=0\r<BR>\n" );
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document.write( "-3x+3y=0<BR>\n" );
document.write( "7x-3y=24\r<BR>\n" );
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document.write( "4x=24\r<BR>\n" );
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document.write( "x=6\r<BR>\n" );
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document.write( "6-y=0<BR>\n" );
document.write( "-y=-6\r<BR>\n" );
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document.write( "y=6\r<BR>\n" );
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document.write( "Problem 3:\r<BR>\n" );
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document.write( "3x-8y=10<BR>\n" );
document.write( "x-4y=3\r<BR>\n" );
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document.write( "-2(x-4y)=-2(3)\r<BR>\n" );
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document.write( "-2x+8y=-6<BR>\n" );
document.write( "3x-8y=10\r<BR>\n" );
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document.write( "x=4\r<BR>\n" );
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document.write( "3(4)-8y=10<BR>\n" );
document.write( "12-8y=10<BR>\n" );
document.write( "-8y=10-12<BR>\n" );
document.write( "-8y=-2\r<BR>\n" );
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document.write( "y=1/4\r<BR>\n" );
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document.write( "Problem 4:\r<BR>\n" );
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document.write( "2x+3y=-5<BR>\n" );
document.write( "3x-y=20\r<BR>\n" );
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document.write( "3(3x-y)=3(20)<BR>\n" );
document.write( "9y-3y=60\r<BR>\n" );
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document.write( "9y-3y=60<BR>\n" );
document.write( "2x+3y=-5\r<BR>\n" );
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document.write( "11x=55\r<BR>\n" );
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document.write( "x=5\r<BR>\n" );
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document.write( "2(5)+3y=-5<BR>\n" );
document.write( "10+3y=-5<BR>\n" );
document.write( "3y=-5-10<BR>\n" );
document.write( "3y=-15\r<BR>\n" );
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document.write( "y=-5\r<BR>\n" );
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document.write( "Thank you\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796334 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "Have I correctly solved the 4 problems below using the systems of simultaneous equations, using either the substitution method or the addition method?\r\n" );
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document.write( "Problem 1\r\n" );
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document.write( "x + 2y = 15\r\n" );
document.write( "x - 2y = -9\r\n" );
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document.write( "2x = 6\r\n" );
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document.write( "x = 3\r\n" );
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document.write( "3 + 2y = 15\r\n" );
document.write( "2y = 15-3\r\n" );
document.write( "2y = 12\r\n" );
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document.write( "y=6\r\n" );
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document.write( "Problem 2:\r\n" );
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document.write( "x - y = 0\r\n" );
document.write( "7x - 3y = 24\r\n" );
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document.write( "-3(x - y) = 0\r\n" );
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document.write( "-3x + 3y = 0\r\n" );
document.write( "7x - 3y = 24\r\n" );
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document.write( "4x = 24\r\n" );
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document.write( "x = 6\r\n" );
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document.write( "6 - y = 0\r\n" );
document.write( "-y = -6\r\n" );
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document.write( "y = 6\r\n" );
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document.write( "Problem 3:\r\n" );
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document.write( "3x - 8y = 10\r\n" );
document.write( "x - 4y = 3\r\n" );
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document.write( "-2(x - 4y) = -2(3)\r\n" );
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document.write( "-2x + 8y = -6\r\n" );
document.write( "3x - 8y = 10\r\n" );
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document.write( "x = 4\r\n" );
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document.write( "3(4) - 8y = 10\r\n" );
document.write( "12 - 8y = 10\r\n" );
document.write( "-8y = 10-12\r\n" );
document.write( "-8y = -2\r\n" );
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document.write( "y = 1/4\r\n" );
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document.write( "Problem 4:\r\n" );
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document.write( "2x + 3y = -5\r\n" );
document.write( "3x - y = 20\r\n" );
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document.write( "3(3x - y) = 3(20)\r\n" );
document.write( "9y - 3y = 60\r\n" );
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document.write( "9y - 3y = 60\r\n" );
document.write( "2x + 3y = -5\r\n" );
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document.write( "11x = 55\r\n" );
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document.write( "x = 5\r\n" );
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document.write( "2(5) + 3y = -5\r\n" );
document.write( "10 + 3y = -5\r\n" );
document.write( "3y = -5-10\r\n" );
document.write( "3y = -15\r\n" );
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document.write( "y = -5\r\n" );
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document.write( "Thank you\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "Hello, &nbsp;I checked every line in your post.\r<BR>\n" );
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document.write( "They &nbsp;ALL &nbsp;are correct.\r<BR>\n" );
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document.write( "Very good job.  &nbsp;My congratulations &nbsp;(!)\r<BR>\n" );
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document.write( "Now, &nbsp;there is another method to check, &nbsp;instead of checking every line.\r<BR>\n" );
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document.write( "After completing the solution, &nbsp;you can / (you should) / (you MUST)  &nbsp;substitute the obtained numbers &nbsp;(the answer)\r<BR>\n" );
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document.write( "into the original equations &nbsp;TO &nbsp;ASSURE &nbsp;that you get valid equalities.\r<BR>\n" );
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document.write( "Such checking is  &nbsp;INDISPENSABLE &nbsp;and &nbsp;NECESSARY &nbsp;part of the solution.\r<BR>\n" );
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document.write( "It is assumed that every student &nbsp;KNOWS &nbsp;about it an &nbsp;MAKES &nbsp;IT &nbsp;after solving each and every such problem.\r<BR>\n" );
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document.write( "Well done (!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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