document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280764>Question 280764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the substitution method {x/8-y/5=1, x/6-y=5} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204051 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=204051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the substitution method {x/8-y/5=1, x/6-y=5}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8+-+y%2F5+=+1 ALIGN=MIDDLE  ALT=\"x%2F8+-+y%2F5+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6+-+y+=+5 ALIGN=MIDDLE  ALT=\"x%2F6+-+y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I would first get rid of the denominators.  For the first equation, multiply everything by 40 (which I found by multiplying the denominator 8 by the denominator 5)\r<BR>\n" );
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document.write( "40<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F8+-+y%2F5%29 ALIGN=MIDDLE  ALT=\"%28x%2F8+-+y%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 40<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29 ALIGN=MIDDLE  ALT=\"%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "5x - 8y = 40  This is the new first equation.  \r<BR>\n" );
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document.write( "I would get rid of the denominator 6 in the 2nd equation by multiplying everything by 6. \r<BR>\n" );
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document.write( "6<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F6+-+y%29 ALIGN=MIDDLE  ALT=\"%28x%2F6+-+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =6<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29 ALIGN=MIDDLE  ALT=\"%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x -6y = 30  This is the new second equation.\r<BR>\n" );
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document.write( "Here are the two equations now:\r<BR>\n" );
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document.write( "5x - 8y = 40<BR>\n" );
document.write( "x -6y = 30 <----- now let's take this equation and solve for \"x\"\r<BR>\n" );
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document.write( "x - 6y = 30<BR>\n" );
document.write( "x = 6y + 30 (added 6y to both sides to isolate the x)<BR>\n" );
document.write( "Now that we know that \"x\" is equal to 6y + 30, let's \"plug\" that into the first equation.  \r<BR>\n" );
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document.write( "5x - 8y = 40  First equation<BR>\n" );
document.write( "5(6y + 30) -8y =40 Plugged in 6y + 30 for the \"x\" variable.<BR>\n" );
document.write( "30y + 150 - 8y =40 Distributed 5 to 6y and 5 to 30.<BR>\n" );
document.write( "22y + 150 = 40 Combined like terms:  30y - 8y = 22y<BR>\n" );
document.write( "22y = 40 - 150 Subtracted 150 from both sides to begin to isolate the y<BR>\n" );
document.write( "22y = -110 Found -110 by determining 40 - 150.<BR>\n" );
document.write( "y = -5 Divided both sides by 22 to isolate the y.  -110 divided by +22 equals -5.\r<BR>\n" );
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document.write( "Now we know that y = -5.  Let's plug that into our 2nd equation.\r<BR>\n" );
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document.write( "x -6y = 30   Second equation<BR>\n" );
document.write( "x -6(-5) = 30 Plugged -5 in for the \"y\" variable.<BR>\n" );
document.write( "x + 30= 30  Determined 30 because -6 times -5 = 30<BR>\n" );
document.write( "x = 30 - 30 Subtracted 30 from both sides to isolate the \"x\"<BR>\n" );
document.write( "x = 0.\r<BR>\n" );
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document.write( "Now we have x = 0 and we have y = -5.\r<BR>\n" );
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document.write( "Let's check:\r<BR>\n" );
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document.write( "Original equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8+-+y%2F5+=+1 ALIGN=MIDDLE  ALT=\"x%2F8+-+y%2F5+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > First original equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F8+-+%28-5%29%2F5+=+1 ALIGN=MIDDLE  ALT=\"0%2F8+-+%28-5%29%2F5+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in the 0 for the X variable and -5 for the y variable.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+5%2F5+=+1 ALIGN=MIDDLE  ALT=\"0+%2B+5%2F5+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5+=+1 ALIGN=MIDDLE  ALT=\"5%2F5+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+1 ALIGN=MIDDLE  ALT=\"1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is correct.  Yay.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6+-+y+=+5 ALIGN=MIDDLE  ALT=\"x%2F6+-+y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Second original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F6+-+%28-5%29+=+5 ALIGN=MIDDLE  ALT=\"0%2F6+-+%28-5%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in 0 for the x variable and -5 for the y variable.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+5+=+5 ALIGN=MIDDLE  ALT=\"0+%2B+5+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+5 ALIGN=MIDDLE  ALT=\"5+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is also correct.  Yay.\r<BR>\n" );
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document.write( "We have proved the answers.  I hope this helps you. :-) </SPAN>\n" );
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