document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112773>Question 112773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by addition or substitution.<BR>\n" );
document.write( "     3x – 4y = 8<BR>\n" );
document.write( "          6x – 2y = 10  <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 #82210 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solving by addition:\r<BR>\n" );
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document.write( "Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4y=8 ALIGN=MIDDLE  ALT=\"3x-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, resulting in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B8y=-16 ALIGN=MIDDLE  ALT=\"-6x%2B8y=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  (Why did I do this step?  Multiplying by a -2 caused the x coefficient to become -6 in this equation so that when we add the two equations, the coefficient on the x term will become zero.  We could just as well have multiplied the second equation by -2 so that the coefficent on the y term would have become -4 and when the two equations were added, the y term coefficient would have become zero.  The arithmetic would be a little different in that case, but the ultimate answer would still be the same.  I'll leave trying it as an exercise for you.)\r<BR>\n" );
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document.write( "Now add the two equations, term by term (the x terms to the x terms, the y terms to the y terms, etc.), resulting in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B6y=-6 ALIGN=MIDDLE  ALT=\"0x%2B6y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=-6 ALIGN=MIDDLE  ALT=\"6y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then substitute the value of y in either of the equations and 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-4%28-1%29=8 ALIGN=MIDDLE  ALT=\"3x-4%28-1%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4=8 ALIGN=MIDDLE  ALT=\"3x%2B4=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=8-4 ALIGN=MIDDLE  ALT=\"3x=8-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284%2F3%29-4%28-1%29=8 ALIGN=MIDDLE  ALT=\"3%284%2F3%29-4%28-1%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B4=8 ALIGN=MIDDLE  ALT=\"4%2B4=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%284%2F3%29-2%28-1%29=10 ALIGN=MIDDLE  ALT=\"6%284%2F3%29-2%28-1%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B2=10 ALIGN=MIDDLE  ALT=\"8%2B2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the answer checks.\r<BR>\n" );
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document.write( "Solve by substitution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4y=8 ALIGN=MIDDLE  ALT=\"3x-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-2y=10 ALIGN=MIDDLE  ALT=\"6x-2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First, rearrange one of the equations so that one of the variable is expressed as a function of the other.  I'll solve the first equation for y.  (Again, it doesn't matter which variable you choose to solve for here -- if you do your arithmetic carefully and follow all of the algebra rules, you get the same answer in the end.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4y=8 ALIGN=MIDDLE  ALT=\"3x-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=-3x%2B8 ALIGN=MIDDLE  ALT=\"-4y=-3x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3x%29%2F%28-4%29%2B8%2F-4 ALIGN=MIDDLE  ALT=\"y=%28-3x%29%2F%28-4%29%2B8%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2F4-2 ALIGN=MIDDLE  ALT=\"y=3x%2F4-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Second, substitute this expression for y into the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-2%283x%2F4-2%29=10 ALIGN=MIDDLE  ALT=\"6x-2%283x%2F4-2%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And then solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-2%283x%2F4-2%29=10 ALIGN=MIDDLE  ALT=\"6x-2%283x%2F4-2%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-3x%2F2%2B4=10 ALIGN=MIDDLE  ALT=\"6x-3x%2F2%2B4=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-3x%2F2=10-4 ALIGN=MIDDLE  ALT=\"6x-3x%2F2=10-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2F2-3x%2F2=6 ALIGN=MIDDLE  ALT=\"12x%2F2-3x%2F2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F2=6 ALIGN=MIDDLE  ALT=\"9x%2F2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x=12 ALIGN=MIDDLE  ALT=\"9x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12%2F9=4%2F3 ALIGN=MIDDLE  ALT=\"x=12%2F9=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, substitute this value for x into either equation and solve for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284%2F3%29-4y=8 ALIGN=MIDDLE  ALT=\"3%284%2F3%29-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-4y=8 ALIGN=MIDDLE  ALT=\"4-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=8-4 ALIGN=MIDDLE  ALT=\"-4y=8-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(4/3,-1) is the solution that we got when we did the problem by addition and we have already checked this answer so you are done.<BR>\n" );
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