document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252508>Question 252508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what multiplier should be used for each of the following equations to eliminate one unknown by subtraction?\r<BR>\n" );
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document.write( "3x-y=7<BR>\n" );
document.write( "2x+7y=42 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184481 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=184481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The multiplier is 7 since this will change -y into -7y. Add this to 7y to get -7+7y=0y=0 which means that it cancels out.\r<BR>\n" );
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document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x-y=7%2C2x%2B7y=42%29 ALIGN=MIDDLE  ALT=\"system%283x-y=7%2C2x%2B7y=42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%283x-y%29=7%287%29 ALIGN=MIDDLE  ALT=\"7%283x-y%29=7%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x-7y=49 ALIGN=MIDDLE  ALT=\"21x-7y=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2821x-7y=49%2C2x%2B7y=42%29 ALIGN=MIDDLE  ALT=\"system%2821x-7y=49%2C2x%2B7y=42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821x-7y%29%2B%282x%2B7y%29=%2849%29%2B%2842%29 ALIGN=MIDDLE  ALT=\"%2821x-7y%29%2B%282x%2B7y%29=%2849%29%2B%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821x%2B2x%29%2B%28-7y%2B7y%29=49%2B42 ALIGN=MIDDLE  ALT=\"%2821x%2B2x%29%2B%28-7y%2B7y%29=49%2B42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23x%2B0y=91 ALIGN=MIDDLE  ALT=\"23x%2B0y=91\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23x=91 ALIGN=MIDDLE  ALT=\"23x=91\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2891%29%2F%2823%29 ALIGN=MIDDLE  ALT=\"x=%2891%29%2F%2823%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x-7y=49 ALIGN=MIDDLE  ALT=\"21x-7y=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2891%2F23%29-7y=49 ALIGN=MIDDLE  ALT=\"21%2891%2F23%29-7y=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=91%2F23 ALIGN=MIDDLE  ALT=\"x=91%2F23\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1911%2F23-7y=49 ALIGN=MIDDLE  ALT=\"1911%2F23-7y=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%281911%2Fcross%2823%29-7y%29=23%2849%29 ALIGN=MIDDLE  ALT=\"23%281911%2Fcross%2823%29-7y%29=23%2849%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1911-161y=1127 ALIGN=MIDDLE  ALT=\"1911-161y=1127\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-161y=1127-1911 ALIGN=MIDDLE  ALT=\"-161y=1127-1911\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1911 ALIGN=MIDDLE  ALT=\"1911\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-161y=-784 ALIGN=MIDDLE  ALT=\"-161y=-784\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-784%29%2F%28-161%29 ALIGN=MIDDLE  ALT=\"y=%28-784%29%2F%28-161%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-161 ALIGN=MIDDLE  ALT=\"-161\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=112%2F23 ALIGN=MIDDLE  ALT=\"y=112%2F23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=91%2F23 ALIGN=MIDDLE  ALT=\"x=91%2F23\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=112%2F23 ALIGN=MIDDLE  ALT=\"y=112%2F23\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Which form the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{91}{23},\frac{112}{23}\right)\">.\r<BR>\n" );
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document.write( "This means that the system is consistent and independent.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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