document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201819>Question 1201819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> X=3y-6<BR>\n" );
document.write( "-4x+9y=9<BR>\n" );
document.write( "Solve either by substation or elemination </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836336 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</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=836336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>(9, 5)</font><BR>\n" );
document.write( "x = 9, y = 5\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "I'll use the substitution method.<BR>\n" );
document.write( "-4x + 9y = 9<BR>\n" );
document.write( "-4( x ) + 9y = 9<BR>\n" );
document.write( "-4( <font color=blue size=4>x</font> ) + 9y = 9<BR>\n" );
document.write( "-4( <font color=blue size=4>3y-6</font> ) + 9y = 9 .... x replaced with 3y-6, valid because x = 3y-6<BR>\n" );
document.write( "-4( 3y-6 ) + 9y = 9<BR>\n" );
document.write( "-4(3y) - 4(-6) + 9y = 9<BR>\n" );
document.write( "-12y + 24 + 9y = 9<BR>\n" );
document.write( "-3y + 24 = 9<BR>\n" );
document.write( "-3y = 9 - 24<BR>\n" );
document.write( "-3y = -15<BR>\n" );
document.write( "y = -15/(-3)<BR>\n" );
document.write( "y = 5\r<BR>\n" );
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document.write( "Use that value of y to determine x.<BR>\n" );
document.write( "x = 3y-6<BR>\n" );
document.write( "x = 3*5-6<BR>\n" );
document.write( "x = 15-6<BR>\n" );
document.write( "x = 9\r<BR>\n" );
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document.write( "The solution as an ordered pair is (x, y) = <font color=red size=4>(9, 5)</font><BR>\n" );
document.write( "Meaning x = 9 and y = 5 pair up together.\r<BR>\n" );
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document.write( "Confirmation with a graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-2%2C12%2C-2%2C12%2C%0D%0Agraph%28400%2C400%2C-2%2C12%2C-2%2C12%2C-100%2C%28x%2B6%29%2F3%2C%289%2B4x%29%2F9%29%2C%0D%0Ared%28%0D%0Acircle%289%2C5%2C0.04%29%2C%0D%0Acircle%289%2C5%2C0.06%29%2C%0D%0Acircle%289%2C5%2C0.08%29%2C%0D%0Acircle%289%2C5%2C0.10%29%2C%0D%0Acircle%289%2C5%2C0.12%29%2C%0D%0Acircle%289%2C5%2C0.14%29%2C%0D%0Alocate%289%2B0.2%2C5-0.2%2C%22%289%2C5%29%22%29%0D%0A%29%2C%0D%0A%0D%0Aline%289%2C0%2C9%2C0.125%29%2Cline%289%2C0.25%2C9%2C0.375%29%2Cline%289%2C0.5%2C9%2C0.625%29%2Cline%289%2C0.75%2C9%2C0.875%29%2Cline%289%2C1%2C9%2C1.125%29%2Cline%289%2C1.25%2C9%2C1.375%29%2Cline%289%2C1.5%2C9%2C1.625%29%2Cline%289%2C1.75%2C9%2C1.875%29%2Cline%289%2C2%2C9%2C2.125%29%2Cline%289%2C2.25%2C9%2C2.375%29%2Cline%289%2C2.5%2C9%2C2.625%29%2Cline%289%2C2.75%2C9%2C2.875%29%2Cline%289%2C3%2C9%2C3.125%29%2Cline%289%2C3.25%2C9%2C3.375%29%2Cline%289%2C3.5%2C9%2C3.625%29%2Cline%289%2C3.75%2C9%2C3.875%29%2Cline%289%2C4%2C9%2C4.125%29%2Cline%289%2C4.25%2C9%2C4.375%29%2Cline%289%2C4.5%2C9%2C4.625%29%2Cline%289%2C4.75%2C9%2C4.875%29%2C%0D%0A%0D%0Aline%280%2C5%2C0.225%2C5%29%2Cline%280.45%2C5%2C0.675%2C5%29%2Cline%280.9%2C5%2C1.125%2C5%29%2Cline%281.35%2C5%2C1.575%2C5%29%2Cline%281.8%2C5%2C2.025%2C5%29%2Cline%282.25%2C5%2C2.475%2C5%29%2Cline%282.7%2C5%2C2.925%2C5%29%2Cline%283.15%2C5%2C3.375%2C5%29%2Cline%283.6%2C5%2C3.825%2C5%29%2Cline%284.05%2C5%2C4.275%2C5%29%2Cline%284.5%2C5%2C4.725%2C5%29%2Cline%284.95%2C5%2C5.175%2C5%29%2Cline%285.4%2C5%2C5.625%2C5%29%2Cline%285.85%2C5%2C6.075%2C5%29%2Cline%286.3%2C5%2C6.525%2C5%29%2Cline%286.75%2C5%2C6.975%2C5%29%2Cline%287.2%2C5%2C7.425%2C5%29%2Cline%287.65%2C5%2C7.875%2C5%29%2Cline%288.1%2C5%2C8.325%2C5%29%2Cline%288.55%2C5%2C8.775%2C5%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 3y-6 in green<BR>\n" );
document.write( "-4x + 9y = 9 in blue<BR>\n" );
document.write( "The two lines intersect at <font color=red size=4>(9, 5)</font> to visually confirm the answer.\r<BR>\n" );
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document.write( "Desmos and GeoGebra are two graphing tools I recommend. Both are free.\r<BR>\n" );
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document.write( "Another way to check (that doesn't involve a graph).\r<BR>\n" );
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document.write( "Plug x = 9 and y = 5 into the first original equation.<BR>\n" );
document.write( "Simplify both sides.<BR>\n" );
document.write( "The goal is to try to get the same number on both sides.<BR>\n" );
document.write( "x = 3y - 6<BR>\n" );
document.write( "9 = 3*5 - 6<BR>\n" );
document.write( "9 = 15-6<BR>\n" );
document.write( "9 = 9 .... confirms the 1st equation\r<BR>\n" );
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document.write( "Repeat for the other original equation<BR>\n" );
document.write( "-4x + 9y = 9<BR>\n" );
document.write( "-4*9 + 9*5 = 9<BR>\n" );
document.write( "-36 + 45 = 9<BR>\n" );
document.write( "9 = 9 .... confirms the 2nd equation\r<BR>\n" );
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document.write( "Both equations are true when x = 9 and y = 5. <BR>\n" );
document.write( "The solution has been fully confirmed.<BR>\n" );
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document.write( " </SPAN>\n" );
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