document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133010>Question 133010</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/003054288X/algebrahomeworkh>Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I can't figure out what the system x=y-4.2 and 2x-3y=-9 can be solved as. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97219 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=97219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y-4.2 ALIGN=MIDDLE  ALT=\"x=y-4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x=10y-42 ALIGN=MIDDLE  ALT=\"10x=10y-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 10 to clear the decimal number\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-10y=-42 ALIGN=MIDDLE  ALT=\"10x-10y=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 10y from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start with the given system of equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2810x-10y=-42%2C2x-3y=-9%29 ALIGN=MIDDLE  ALT=\"system%2810x-10y=-42%2C2x-3y=-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's isolate y in the first equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-10y=-42 ALIGN=MIDDLE  ALT=\"10x-10y=-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10y=-42-10x ALIGN=MIDDLE  ALT=\"-10y=-42-10x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x ALIGN=MIDDLE  ALT=\"10x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10y=-10x-42 ALIGN=MIDDLE  ALT=\"-10y=-10x-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-10x-42%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"y=%28-10x-42%29%2F%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10 ALIGN=MIDDLE  ALT=\"-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-10%29%2F%28-10%29%29x%2B%28-42%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"y=%28%28-10%29%2F%28-10%29%29x%2B%28-42%29%2F%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3highlight%28%28x%2B21%2F5%29%29=-9 ALIGN=MIDDLE  ALT=\"2x-3highlight%28%28x%2B21%2F5%29%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B%28-3%29%281%29x%2B%28-3%29%2821%2F5%29=-9 ALIGN=MIDDLE  ALT=\"2x%2B%28-3%29%281%29x%2B%28-3%29%2821%2F5%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3x-63%2F5=-9 ALIGN=MIDDLE  ALT=\"2x-3x-63%2F5=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%282x-3x-63%2F5%29=%285%29%28-9%29 ALIGN=MIDDLE  ALT=\"%285%29%282x-3x-63%2F5%29=%285%29%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 5. 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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-15x-63=-45 ALIGN=MIDDLE  ALT=\"10x-15x-63=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply the LCM to each side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x-63=-45 ALIGN=MIDDLE  ALT=\"-5x-63=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x=-45%2B63 ALIGN=MIDDLE  ALT=\"-5x=-45%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 63 to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x=18 ALIGN=MIDDLE  ALT=\"-5x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2818%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"x=%2818%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -5 to isolate x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-18%2F5 ALIGN=MIDDLE  ALT=\"x=-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------First Answer------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the first part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-18%2F5 ALIGN=MIDDLE  ALT=\"x=-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-18%2F5 ALIGN=MIDDLE  ALT=\"x=-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can plug it into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we previously solved 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;\" > in the first equation).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=x%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > was previously isolated.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-18%2F5%29%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=%28-18%2F5%29%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-18%2F5 ALIGN=MIDDLE  ALT=\"x=-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-18%2F5%2B21%2F5 ALIGN=MIDDLE  ALT=\"y=-18%2F5%2B21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms  (note: if you need help with fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a>)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------Second Answer------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the second part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------Summary------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our answers are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-18%2F5 ALIGN=MIDDLE  ALT=\"x=-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which form the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\frac{18}{5},\frac{3}{5}\right)\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );