document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515347>Question 515347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please solve the following by graphing. Demonstrate on the graph what the solution means. Then solve algebraically by substitution and then<BR>\n" );
document.write( "again by the addition property of equality?\r<BR>\n" );
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document.write( "2x + y = 6<BR>\n" );
document.write( "y - x = -3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343922 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=343922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, you have to recognize that you have linear equations.<BR>\n" );
document.write( "The addition and subtraction property of equality is that:<BR>\n" );
document.write( "if a = b, then a+c = b+c, and a-c = b-c.<BR>\n" );
document.write( "You often use this property in solving problems.<BR>\n" );
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document.write( "2x + y = 6<BR>\n" );
document.write( "y -x = -3<BR>\n" );
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document.write( "rearranged...<BR>\n" );
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document.write( "2x + y = 6<BR>\n" );
document.write( "-x +y = -3<BR>\n" );
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document.write( "subtract the 2nd equation from the 1st and you get:<BR>\n" );
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document.write( "3x = 9<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "substitute x=3 to find y<BR>\n" );
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document.write( "2x + y = 6<BR>\n" );
document.write( "2(3) + y = 6<BR>\n" );
document.write( "6 + y = 6<BR>\n" );
document.write( "y = 0<BR>\n" );
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document.write( "So, the lines intersect at:  (3,0)<BR>\n" );
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document.write( "Or you could have solved by elimination.<BR>\n" );
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document.write( "Gien y-x =-3<BR>\n" );
document.write( "y -x+x = -3+x  (the addition property)<BR>\n" );
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document.write( "y = -3+3 = 0<BR>\n" );
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document.write( "substitute y=0 to find x<BR>\n" );
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document.write( "2x +y = 6<BR>\n" );
document.write( "2x +0 = 6<BR>\n" );
document.write( "2x = 6<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "Again, this tells us the lines intersect at (3,0).<BR>\n" );
document.write( "Another way of saying this is that the point (3,0) satisfies both equations.<BR>\n" );
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document.write( "To graph it is easiest to use the slope-intercept form:<BR>\n" );
document.write( "2x + y = 6<BR>\n" );
document.write( "y -x = -3<BR>\n" );
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document.write( "which become<BR>\n" );
document.write( "y = -2x +6<BR>\n" );
document.write( "y = x-3<BR>\n" );
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document.write( "In this graph the first equation is red and the second is green.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2%2Ax%2B6%2Cx-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2%2Ax%2B6%2Cx-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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