document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188887>Question 188887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solving systems of linear equations.solve by substitution\r<BR>\n" );
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document.write( "2x+y=10<BR>\n" );
document.write( "3x-4y=26\r<BR>\n" );
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document.write( "y=2x+3<BR>\n" );
document.write( "3x+2y=6\r<BR>\n" );
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document.write( "solving systems of linear equations.solve by addition elimination\r<BR>\n" );
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document.write( "3x-6y=5<BR>\n" );
document.write( "2x-4y=8\r<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 #141679 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=141679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face\"Tahoma\" size=1.5><BR>\n" );
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document.write( "Solving systems of linear equations.Solve by substitution <BR>\n" );
document.write( "2x+y=10, EQN 1<BR>\n" );
document.write( "3x-4y=26, EQN 2\r<BR>\n" );
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document.write( "In EQN 1 we get, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10-2x ALIGN=MIDDLE  ALT=\"y=10-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> EQN 3, substitute in EQN 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4%28highlight%2810-2x%29%29=26 ALIGN=MIDDLE  ALT=\"3x-4%28highlight%2810-2x%29%29=26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-40%2B8x=26 ALIGN=MIDDLE  ALT=\"3x-40%2B8x=26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x=26%2B40=66 ALIGN=MIDDLE  ALT=\"11x=26%2B40=66\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2811%29x%2Fcross%2811%29=cross%2866%296%2Fcross%2811%29 ALIGN=MIDDLE  ALT=\"cross%2811%29x%2Fcross%2811%29=cross%2866%296%2Fcross%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute in EQN 3:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10-2%286%29=10-12=highlight%28-2%29 ALIGN=MIDDLE  ALT=\"y=10-2%286%29=10-12=highlight%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Intersect at point <font color=blue>(6,-2)</font><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C10%2C-8%2C5%2Cgraph%28300%2C300%2C-4%2C10%2C-8%2C5%2C10-2x%2C%283x-26%29%2F4%29%2Cblue%28circle%286%2C-2%2C.15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---><font color=red>RED, EQN1</font>; <font color=green>GREEN, EQN 2</font>\r<BR>\n" );
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document.write( "y=2x+3, EQN 1<BR>\n" );
document.write( "3x+2y=6, EQN 2\r<BR>\n" );
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document.write( "Substitute EQN 1 in EQN 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2highlight%28%282x%2B3%29%29=6 ALIGN=MIDDLE  ALT=\"3x%2B2highlight%28%282x%2B3%29%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4x%2B6=6 ALIGN=MIDDLE  ALT=\"3x%2B4x%2B6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=6-6=0 ALIGN=MIDDLE  ALT=\"7x=6-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=0%29 ALIGN=MIDDLE  ALT=\"highlight%28x=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, subst. in EQN 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%280%29%2B3 ALIGN=MIDDLE  ALT=\"y=2%280%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Intersect at point <font color=blue>(0,3)</font><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C10%2C-8%2C5%2Cgraph%28300%2C300%2C-4%2C10%2C-8%2C5%2C2x%2B3%2C%286-3x%29%2F2%29%2Cblue%28circle%280%2C3%2C.15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <font color=red>RED, EQN 1</font>;<font color=green> GREEN, EQN 2</font>\r<BR>\n" );
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document.write( "Solving systems of linear equations. Solve by addition elimination <BR>\n" );
document.write( "3x-6y=5, EQN 1<BR>\n" );
document.write( "2x-4y=8, EQN 2 \r<BR>\n" );
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document.write( "Multiply EQN 1 by -4, EQN 2 by 6, and then \"add\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-6y=5 ALIGN=MIDDLE  ALT=\"3x-6y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28-12x%29%2Bcross%2824y%29=-20 ALIGN=MIDDLE  ALT=\"cross%28-12x%29%2Bcross%2824y%29=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y=8 ALIGN=MIDDLE  ALT=\"2x-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2812x%29-cross%2824y%29=48 ALIGN=MIDDLE  ALT=\"cross%2812x%29-cross%2824y%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\ \ \ \ \ \ \ \ \ \ \ \ \ -------------------\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0=28\"> no solution. These lines don't intersect:\r<BR>\n" );
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document.write( "We'll look for the intercepts:<BR>\n" );
document.write( "In EQN 1, let fy=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-6%280%29=5 ALIGN=MIDDLE  ALT=\"3x-6%280%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283%29x%2Fcross%283%29=5%2F3 ALIGN=MIDDLE  ALT=\"cross%283%29x%2Fcross%283%29=5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=5%2F3%29 ALIGN=MIDDLE  ALT=\"red%28x=5%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "let fx=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%280%29-6y=5 ALIGN=MIDDLE  ALT=\"3%280%29-6y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28-6%29y%2Fcross%28-6%29=5%2F-6 ALIGN=MIDDLE  ALT=\"cross%28-6%29y%2Fcross%28-6%29=5%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=-5%2F6%29 ALIGN=MIDDLE  ALT=\"red%28y=-5%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In EQN 2, let Fy=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4%280%29=8 ALIGN=MIDDLE  ALT=\"2x-4%280%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282%29x%2Fcross%282%29=cross%288%294%2Fcross%282%29 ALIGN=MIDDLE  ALT=\"cross%282%29x%2Fcross%282%29=cross%288%294%2Fcross%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=4%29 ALIGN=MIDDLE  ALT=\"red%28x=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let fx=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%29-4y=8 ALIGN=MIDDLE  ALT=\"2%280%29-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28-4%29y%2Fcross%28-4%29=cross%288%292%2Fcross%28-4%29 ALIGN=MIDDLE  ALT=\"cross%28-4%29y%2Fcross%28-4%29=cross%288%292%2Fcross%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=-2%29 ALIGN=MIDDLE  ALT=\"red%28y=-2%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=drawing%28300%2C300%2C-4%2C10%2C-8%2C5%2Cgraph%28300%2C300%2C-4%2C10%2C-8%2C5%2C%283x-5%29%2F6%2C%282x-8%29%2F4%29%2Cblue%28circle%285%2F3%2C0%2C.15%29%29%2Cblue%28circle%280%2C-5%2F6%2C.15%29%29%2Cblue%28circle%284%2C0%2C.15%29%29%2Cblue%28circle%280%2C-2%2C.15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <font color=red>RED, </font>EQN 1; <font color=green>GREEN, EQN 2</font><BR>\n" );
document.write( "Since they line on the same plane they are parallel\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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