document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=46819>Question 46819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the simultaneous equations:\r<BR>\n" );
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document.write( "y=x^2+2x+9<BR>\n" );
document.write( "7x+y=19\r<BR>\n" );
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document.write( "please show me how u solve it. thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31012 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=31012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the simultaneous equations (aka: System of equations):<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2B2x%2B9 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2B2x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2By+=+19 ALIGN=MIDDLE  ALT=\"7x%2By+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can solve this system of equations (aka: Simultaneous equations) by the \"susbtitution\" method.<BR>\n" );
document.write( "Substitute equation 1) into equation 2) for y and solve for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+%2B+%28x%5E2%2B2x%2B9%29+=+19 ALIGN=MIDDLE  ALT=\"7x+%2B+%28x%5E2%2B2x%2B9%29+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9x%2B9+=+19 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x%2B9+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 19 from both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9x-10+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x-10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve this quadratic equation by factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%2B10%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%2B10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=+0 ALIGN=MIDDLE  ALT=\"x-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B10+=+0 ALIGN=MIDDLE  ALT=\"x%2B10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=+0 ALIGN=MIDDLE  ALT=\"x-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <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;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B10+=+0 ALIGN=MIDDLE  ALT=\"x%2B10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-10 ALIGN=MIDDLE  ALT=\"x+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, to find the value of y, substitute the values of x, one-at-a-time into either of the two original equations and solve for y. Let's take the first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2B2x%2B9 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2B2x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute x = 1 then solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%5E2%2B2%281%29%2B9 ALIGN=MIDDLE  ALT=\"y+=+1%5E2%2B2%281%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12 ALIGN=MIDDLE  ALT=\"y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So one of the solutions is: x = 1, y = 12 or (1,12)\r<BR>\n" );
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document.write( "Just as a check, you can see that, had we substituted x = 1 into the second equation, we would have obtained the same result.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%281%29+%2B+y+=+19 ALIGN=MIDDLE  ALT=\"7%281%29+%2B+y+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtact 7 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12 ALIGN=MIDDLE  ALT=\"y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Same as before.\r<BR>\n" );
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document.write( "Now to get the second solution, substitute x = -10 into the first equation and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-10%29%5E2%2B2%28-10%29%2B9 ALIGN=MIDDLE  ALT=\"y+=+%28-10%29%5E2%2B2%28-10%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100-20%2B9 ALIGN=MIDDLE  ALT=\"y+=+100-20%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+89 ALIGN=MIDDLE  ALT=\"y+=+89\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's try using the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28-10%29+%2B+y+=+19 ALIGN=MIDDLE  ALT=\"7%28-10%29+%2B+y+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-70+%2B+y+=+19 ALIGN=MIDDLE  ALT=\"-70+%2B+y+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 70 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+89 ALIGN=MIDDLE  ALT=\"y+=+89\"   DISABLED_style= \"max-width:90%; height:auto;\" > Same as before.\r<BR>\n" );
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document.write( "The second solution is: x = -10, y = 89 or (-10, 89}\r<BR>\n" );
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document.write( " </SPAN>\n" );
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