document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171442>Question 1171442</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this equation:<BR>\n" );
document.write( "A.	Determine the type of system (inconsistent, consistent and independent, consistent and dependent) using algebraic methods and state the number of solutions.<BR>\n" );
document.write( "B.	Solve each system graphically and give the solution/s (if coinciding, give 2) and verify.<BR>\n" );
document.write( "C.	Solve each system by using substitution method.<BR>\n" );
document.write( "D.	Solve each system by using elimination method.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%2B4y=8+ ALIGN=MIDDLE  ALT=\"+2x%2B4y=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%2B12y=24++ ALIGN=MIDDLE  ALT=\"+6x%2B12y=24++\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796383 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equations are consistent and dependent.<BR>\n" );
document.write( "this means they are identical and make the same graph.<BR>\n" );
document.write( "here's a graph of the equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/120902.jpg\" >\r<BR>\n" );
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document.write( "as you can see, they make the same line on the graph.<BR>\n" );
document.write( "that's because the equations are identical.\r<BR>\n" );
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document.write( "to solve this system of equations by the substitution method, do the following:<BR>\n" );
document.write( "2x + 4y = 8<BR>\n" );
document.write( "6x + 12y = 24<BR>\n" );
document.write( "solve for y in the first eqution to get:<BR>\n" );
document.write( "y = (8-2x)/4<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "y = 2 - .5x<BR>\n" );
document.write( "replace y with 2 - .5x in the second equation to get:<BR>\n" );
document.write( "6x + 12 * (2 - .5x) = 24<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "6x + 42 - 6x = 24<BR>\n" );
document.write( "combine like terms to get 24 = 24.<BR>\n" );
document.write( "since the variables disappeared and the equation is true, then you have a consistent and dependent solution, meaning the equations are identical.\r<BR>\n" );
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document.write( "to solve this system of equations by the elimination method, do the following:<BR>\n" );
document.write( "2x + 4y = 8<BR>\n" );
document.write( "6x + 12y = 24<BR>\n" );
document.write( "multiply both sides of the first equation by 3 and leave the second equation as is to get:<BR>\n" );
document.write( "6x + 12y = 24<BR>\n" );
document.write( "6x + 12y = 24<BR>\n" );
document.write( "subtract the second equation from the first to get:<BR>\n" );
document.write( "0 + 0 = 0<BR>\n" );
document.write( "since the variables disappeared and the equation is still true, you have identical equations.\r<BR>\n" );
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document.write( "here's a reference.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.jamesbrennan.org/algebra/systems/solution_set.htm\" target = \"_blank\">https://www.jamesbrennan.org/algebra/systems/solution_set.htm</a>\r<BR>\n" );
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