document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428586>Question 428586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by graphing and then get an exact solution by using either substitution or elimination. (if you cant graph please just answer the second part)\r<BR>\n" );
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document.write( "   y=2/3x+3<BR>\n" );
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document.write( "   3x-3y=-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297867 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=297867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equations are:\r<BR>\n" );
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document.write( "y = (2/3)*x + 3\r<BR>\n" );
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document.write( "and:\r<BR>\n" );
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document.write( "3x - 3y = -6\r<BR>\n" );
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document.write( "in order to graph these equations, you need to solve for y.\r<BR>\n" );
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document.write( "the first one is already solved for y.\r<BR>\n" );
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document.write( "the second one is solved for y in the following manner:\r<BR>\n" );
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document.write( "3x - 3y = -6<BR>\n" );
document.write( "subtract 3x from both sides of the equation to get:<BR>\n" );
document.write( "-3y = -3x - 6<BR>\n" );
document.write( "divide both sides of the equation by -3 to get:<BR>\n" );
document.write( "y = (-3/-3)*x - (6/-3)<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "y = x - (-2)<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "y = x + 2\r<BR>\n" );
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document.write( "the 2 equations that you can now graph are:\r<BR>\n" );
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document.write( "y = (2/3)x + 3<BR>\n" );
document.write( "y = x + 2\r<BR>\n" );
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document.write( "the graph of these equations is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-2%2C8%2C%282%2F3%29%2Ax%2B3%2Cx%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-2%2C8%2C%282%2F3%29%2Ax%2B3%2Cx%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the graph shows an intersection at somewhere around x = 3 and y = 5.\r<BR>\n" );
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document.write( "you can solve these equations by substitution to see if the answer comes out somewhere near there.\r<BR>\n" );
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document.write( "use the original equations of:\r<BR>\n" );
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document.write( "y = (2/3)x + 3<BR>\n" );
document.write( "3x - 3y = -6\r<BR>\n" );
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document.write( "since your first equation has already solved for y, you can use that to substitute for y in the second equation to get:\r<BR>\n" );
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document.write( "3x - 3y = -6 becomes 3x - 3*((2/3)x + 3) = -6\r<BR>\n" );
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document.write( "simplify by removing parentheses to get:\r<BR>\n" );
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document.write( "3x - 3*(2/3)x - 3*3 = -6\r<BR>\n" );
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document.write( "simpify further to get:\r<BR>\n" );
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document.write( "3x - 2x - 9 = -6\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "x - 9 = -6\r<BR>\n" );
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document.write( "add 9 to both sides of the equation to gert:\r<BR>\n" );
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document.write( "x = -6 + 9\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "x = 3\r<BR>\n" );
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document.write( "you now have x = 3 and you can substitute for x in either equation to solve for y.\r<BR>\n" );
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document.write( "we'll use the first equation.\r<BR>\n" );
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document.write( "the first equation is y = (2/3)x + 3\r<BR>\n" );
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document.write( "substitute 3 for x to get:\r<BR>\n" );
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document.write( "y = (2/3)*3 + 3\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y = 2 + 3 which becomes y = 5\r<BR>\n" );
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document.write( "your solution for this set of simultaneous equations is:\r<BR>\n" );
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document.write( "x = 3<BR>\n" );
document.write( "y = 5\r<BR>\n" );
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document.write( "this is confirmed by the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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