document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145836>Question 145836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by the elimination method<BR>\n" );
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document.write( "0.3x-0.2y=4<BR>\n" );
document.write( "0.5x+0.3y=5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106425 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=106425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3x-0.2y=4 ALIGN=MIDDLE  ALT=\"0.3x-0.2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%280.3x-0.2y%29=10%284%29 ALIGN=MIDDLE  ALT=\"10%280.3x-0.2y%29=10%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 10 to move the decimal on each number 1 time. This will make every number a whole number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=40 ALIGN=MIDDLE  ALT=\"3x-2y=40\"   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=0.5x%2B0.3y=5 ALIGN=MIDDLE  ALT=\"0.5x%2B0.3y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%280.5x%2B0.3y%29=10%285%29 ALIGN=MIDDLE  ALT=\"10%280.5x%2B0.3y%29=10%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 10 to move the decimal on each number 1 time. This will make every number a whole number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y=50 ALIGN=MIDDLE  ALT=\"5x%2B3y=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply\r<BR>\n" );
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document.write( "So we now have the system of equations:\r<BR>\n" );
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document.write( "Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we would have to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or vice versa).\r<BR>\n" );
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document.write( "So lets eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In order to do that, we need to have both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.\r<BR>\n" );
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document.write( "So to make the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients equal in magnitude but opposite in sign, we need to multiply both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients by some number to get them to an common number. So if we wanted to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to some equal number, we could try to get them to the LCM.\r<BR>\n" );
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document.write( "Since the LCM of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to multiply both sides of the top equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and multiply both sides of the bottom equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%283x-2y%29=5%2840%29 ALIGN=MIDDLE  ALT=\"5%283x-2y%29=5%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the top equation (both sides) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%285x%2B3y%29=-3%2850%29 ALIGN=MIDDLE  ALT=\"-3%285x%2B3y%29=-3%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the bottom equation (both sides) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x-10y=200 ALIGN=MIDDLE  ALT=\"15x-10y=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now add the equations together. In order to add 2 equations, group like terms and combine them\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x-15x%29%2B%28-10y-9y%29=200-150 ALIGN=MIDDLE  ALT=\"%2815x-15x%29%2B%28-10y-9y%29=200-150\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combine like terms and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2815x-15x%29-19y=50 ALIGN=MIDDLE  ALT=\"cross%2815x-15x%29-19y=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how the x terms cancel out\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19y=50 ALIGN=MIDDLE  ALT=\"-19y=50\"   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=y=50%2F-19 ALIGN=MIDDLE  ALT=\"y=50%2F-19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19 ALIGN=MIDDLE  ALT=\"-19\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-50%2F19 ALIGN=MIDDLE  ALT=\"y=-50%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=40 ALIGN=MIDDLE  ALT=\"3x-2y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=40 ALIGN=MIDDLE  ALT=\"3x-2y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2%28-50%2F19%29=40 ALIGN=MIDDLE  ALT=\"3x-2%28-50%2F19%29=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-50%2F19 ALIGN=MIDDLE  ALT=\"y=-50%2F19\"   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=3x%2B100%2F19=40 ALIGN=MIDDLE  ALT=\"3x%2B100%2F19=40\"   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=%2819%29%283x%2B100%2F19%29=%2819%29%2840%29 ALIGN=MIDDLE  ALT=\"%2819%29%283x%2B100%2F19%29=%2819%29%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 19. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=57x%2B100=760 ALIGN=MIDDLE  ALT=\"57x%2B100=760\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply the LCM to each side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=57x=760-100 ALIGN=MIDDLE  ALT=\"57x=760-100\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 100 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=57x=660 ALIGN=MIDDLE  ALT=\"57x=660\"   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=x=%28660%29%2F%2857%29 ALIGN=MIDDLE  ALT=\"x=%28660%29%2F%2857%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 57 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=220%2F19 ALIGN=MIDDLE  ALT=\"x=220%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So our answers are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=220%2F19 ALIGN=MIDDLE  ALT=\"x=220%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-50%2F19 ALIGN=MIDDLE  ALT=\"y=-50%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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