document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120350>Question 120350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i dont kno0w how to sove for substitution elimination or graphing for this problem 2x-y=1 and 3x+y=-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88227 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b><big>Substitution:</b></big>\r<BR>\n" );
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document.write( "Eq. 1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=1 ALIGN=MIDDLE  ALT=\"2x-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq. 2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=-6 ALIGN=MIDDLE  ALT=\"3x%2By=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve equation 1 for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=1 ALIGN=MIDDLE  ALT=\"2x-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=-2x%2B1 ALIGN=MIDDLE  ALT=\"-y=-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-1 ALIGN=MIDDLE  ALT=\"y=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the expression just developed for y and substitute it into equation 2 in place of the y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=-6 ALIGN=MIDDLE  ALT=\"3x%2By=-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%2B%282x-1%29=-6 ALIGN=MIDDLE  ALT=\"3x%2B%282x-1%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B%282x-1%29=-6 ALIGN=MIDDLE  ALT=\"3x%2B%282x-1%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=5x-1=-6 ALIGN=MIDDLE  ALT=\"5x-1=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=-6%2B1 ALIGN=MIDDLE  ALT=\"5x=-6%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=-5 ALIGN=MIDDLE  ALT=\"5x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >}\r<BR>\n" );
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document.write( "Substitute this value for x into equation 1 and solve for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-1%29-y=1 ALIGN=MIDDLE  ALT=\"2%28-1%29-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-y=1 ALIGN=MIDDLE  ALT=\"-2-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=1%2B2 ALIGN=MIDDLE  ALT=\"-y=1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore the solution set is the ordered pair (-1,-3)\r<BR>\n" );
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document.write( "<b><big>Elimination:</b></big>\r<BR>\n" );
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document.write( "Eq. 1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=1 ALIGN=MIDDLE  ALT=\"2x-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq. 2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=-6 ALIGN=MIDDLE  ALT=\"3x%2By=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add the two equations term-by-term:\r<BR>\n" );
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document.write( "Sum:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=-5 ALIGN=MIDDLE  ALT=\"5x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since you have a -y in one equation and a y in the other, you can add the two equations directly to eliminate the y variable.  In other problems where the coefficients are not direct additive inverses on one of the variables, you will have to multiply through one of the equations by an appropriate value to create the additive inverse situation.\r<BR>\n" );
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document.write( "To illustrate the process, I'll solve for the y variable by elimination of the x variable:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=1 ALIGN=MIDDLE  ALT=\"2x-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=-6 ALIGN=MIDDLE  ALT=\"3x%2By=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply equation 1 by 3, and equation 2 by -2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-3y=3 ALIGN=MIDDLE  ALT=\"6x-3y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-2y=12 ALIGN=MIDDLE  ALT=\"-6x-2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations term by term:\r<BR>\n" );
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document.write( "Sum: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y=15 ALIGN=MIDDLE  ALT=\"-5y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And solve for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again, the solution set is the ordered pair (-1,-3)  (And I sincerely hope you aren't surprised that the two methods produce the same result.  I wouldn't have been surprised necessarily if they had been different, but I would have been supremely confident that I had made an error in the performance of one or both of the methods.)\r<BR>\n" );
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document.write( "<b><big>Graphing:</b></big>\r<BR>\n" );
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document.write( "Select two x values for each of the lines, and then compute the corresponding y value for each selected x.  This will give you two ordered pairs for each line.  Plot the points and construct a straight line through each set of points.  The solution will be where the two lines intersect.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x-1%2C-3x-6%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x-1%2C-3x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And, as we suspected, the point of intersection is (-1,-3)\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );