document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196710>Question 1196710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is an ordered pair for 5x - 2y = 12 and -5x + 6y = -56<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 #829773 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given System of Equations<BR>\n" );
document.write( "5x-2y = 12<BR>\n" );
document.write( "-5x+6y = -56\r<BR>\n" );
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document.write( "Add the equations straight down<BR>\n" );
document.write( "The x terms cancel out (since 5x+(-5x) = 0x = 0)<BR>\n" );
document.write( "The y terms combine to 4y<BR>\n" );
document.write( "The right hand sides combine to -44\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "4y = -44<BR>\n" );
document.write( "y = -44/4<BR>\n" );
document.write( "y = -11\r<BR>\n" );
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document.write( "Use this to find x.<BR>\n" );
document.write( "Pick either equation to plug in y = -11<BR>\n" );
document.write( "I'll select the first equation<BR>\n" );
document.write( "5x-2y = 12<BR>\n" );
document.write( "5x-2(-11) = 12<BR>\n" );
document.write( "5x+22 = 12<BR>\n" );
document.write( "5x = 12-22<BR>\n" );
document.write( "5x = -10<BR>\n" );
document.write( "x = -10/5<BR>\n" );
document.write( "x = -2\r<BR>\n" );
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document.write( "We have x = -2 and y = -11 pairing up together to get us <font color=red>the ordered pair solution (x,y) = (-2,-11)</font>\r<BR>\n" );
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document.write( "We can confirm this through a graph<BR>\n" );
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document.write( "Here's the link to the interactive page<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/doa1oqrje8\">https://www.desmos.com/calculator/doa1oqrje8</a><BR>\n" );
document.write( "Desmos is a free graphing app that I use often.<BR>\n" );
document.write( "GeoGebra is another free graphing app I use all the time as well.\r<BR>\n" );
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document.write( "Notes:<BR>\n" );
document.write( "5x-2y = 12 goes through the points (0,-6) and (2,-1)<BR>\n" );
document.write( "-5x+6y = -56 goes through the points (4,-6) and (10,-1)\r<BR>\n" );
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document.write( "------------------------------------------------------\r<BR>\n" );
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document.write( "A non-visual way to check the answer:\r<BR>\n" );
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document.write( "Plug (x,y) = (-2,-11) into the first equation<BR>\n" );
document.write( "5x-2y = 12<BR>\n" );
document.write( "5(-2)-2(-11) = 12<BR>\n" );
document.write( "-10+22 = 12<BR>\n" );
document.write( "12 = 12<BR>\n" );
document.write( "We get a true statement.\r<BR>\n" );
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document.write( "Do the same for the second equation<BR>\n" );
document.write( "-5x+6y = -56<BR>\n" );
document.write( "-5(-2)+6(-11) = -56<BR>\n" );
document.write( "10-66 = -56<BR>\n" );
document.write( "-56 = -56<BR>\n" );
document.write( "The second equation is confirmed as well.\r<BR>\n" );
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document.write( "Both equations are true when we plug in x = -2 and y = -11.<BR>\n" );
document.write( "Therefore, the solution has been fully confirmed.\r<BR>\n" );
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document.write( "We can use WolframAlpha to help confirm the answer<BR>\n" );
document.write( "In the search bar, type in <font color=red>5x - 2y = 12 and -5x + 6y = -56</font> <BR>\n" );
document.write( "You could replace the \"and\" with a comma if you prefer.<BR>\n" );
document.write( "This is what you should get<BR>\n" );
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document.write( "Here's the link<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.wolframalpha.com/input?i=5x+-+2y+%3D+12+and+-5x+%2B+6y+%3D+-56\">https://www.wolframalpha.com/input?i=5x+-+2y+%3D+12+and+-5x+%2B+6y+%3D+-56</a><BR>\n" );
document.write( "WolframAlpha offers a graph, though it may be in a format you are unfamiliar with. <BR>\n" );
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document.write( "Notice the graphing window doesn't have the origin anywhere in view. This is because we're centered more around (-2,-11) which places us southwest of the origin. The good news is that the numbers along the side should help pinpoint where we are.\r<BR>\n" );
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document.write( "There are other software tools to quickly check the answer. With GeoGebra, you would type in <font color=red>Solve[{5x - 2y = 12,-5x + 6y = -56}]</font><BR>\n" );
document.write( "The use of square brackets and curly braces are necessary. Feel free to explore your favorite software option to check the answer. <BR>\n" );
document.write( "Though please don't rely on the software to replace your brain and do your homework for you. You'll still need practice when the exams happen.<BR>\n" );
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