document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204629>Question 1204629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y = x - 8<BR>\n" );
document.write( "y = -2x + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841029 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<font color=red size=4>Answer:</font> (x,y) = (3, -5)\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "I'll graph each equation to show how to get that answer.<BR>\n" );
document.write( "You can use a graphing tool like Desmos or GeoGebra to quickly get the answer, but I'll show the step-by-step process by hand.\r<BR>\n" );
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document.write( "To graph each line, we plot two points.<BR>\n" );
document.write( "Each point is of the form (x,y)<BR>\n" );
document.write( "We select any x value we want to get its paired y value.\r<BR>\n" );
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document.write( "Plug x = 0 into the 1st equation.<BR>\n" );
document.write( "y = x-8<BR>\n" );
document.write( "y = 0-8<BR>\n" );
document.write( "y = -8<BR>\n" );
document.write( "The point (0,-8) is on the line y = x-8\r<BR>\n" );
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document.write( "Repeat for x = 1<BR>\n" );
document.write( "y = x-8<BR>\n" );
document.write( "y = 1-8<BR>\n" );
document.write( "y = -7<BR>\n" );
document.write( "The point (1,-7) is also on the line y = x-8\r<BR>\n" );
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document.write( "Plot the two points (0,-8) and (1,-7) to graph the line y = x-8.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-3%2C12%2C-12%2C2%2C%0D%0Agraph%28400%2C400%2C-3%2C12%2C-12%2C2%2C-100%2Cx-8%29%2C%0D%0A%0D%0Acircle%280%2C-8%2C0.05%29%2Ccircle%280%2C-8%2C0.07%29%2Ccircle%280%2C-8%2C0.09%29%2Ccircle%280%2C-8%2C0.11%29%2Ccircle%280%2C-8%2C0.13%29%2Ccircle%280%2C-8%2C0.15%29%2Ccircle%280%2C-8%2C0.17%29%2Ccircle%280%2C-8%2C0.19%29%2Ccircle%281%2C-7%2C0.05%29%2Ccircle%281%2C-7%2C0.07%29%2Ccircle%281%2C-7%2C0.09%29%2Ccircle%281%2C-7%2C0.11%29%2Ccircle%281%2C-7%2C0.13%29%2Ccircle%281%2C-7%2C0.15%29%2Ccircle%281%2C-7%2C0.17%29%2Ccircle%281%2C-7%2C0.19%29%2C%0D%0A%0D%0Alocate%280%2B0.1%2C-8-0.1%2C%22%280%2C-8%29%22%29%2C%0D%0Alocate%281%2B0.1%2C-7-0.1%2C%22%281%2C-7%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Repeat similar steps for the other equation. Two points on the line y = -2x+1 are (0,1) and (1,-1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-3%2C12%2C-6%2C6%2C%0D%0Agraph%28400%2C400%2C-3%2C12%2C-6%2C6%2C-100%2C-100%2C-2x%2B1%29%2C%0D%0A%0D%0Acircle%280%2C1%2C0.05%29%2Ccircle%280%2C1%2C0.07%29%2Ccircle%280%2C1%2C0.09%29%2Ccircle%280%2C1%2C0.11%29%2Ccircle%280%2C1%2C0.13%29%2Ccircle%280%2C1%2C0.15%29%2Ccircle%280%2C1%2C0.17%29%2Ccircle%280%2C1%2C0.19%29%2Ccircle%281%2C-1%2C0.05%29%2Ccircle%281%2C-1%2C0.07%29%2Ccircle%281%2C-1%2C0.09%29%2Ccircle%281%2C-1%2C0.11%29%2Ccircle%281%2C-1%2C0.13%29%2Ccircle%281%2C-1%2C0.15%29%2Ccircle%281%2C-1%2C0.17%29%2Ccircle%281%2C-1%2C0.19%29%2C%0D%0A%0D%0Alocate%280%2B0.3%2C1%2B0.1%2C%22%280%2C1%29%22%29%2C%0D%0Alocate%281%2B0.3%2C-1%2B0.1%2C%22%281%2C-1%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's plot the two lines together on the same xy grid.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-3%2C12%2C-9%2C6%2C%0D%0Agraph%28400%2C400%2C-3%2C12%2C-9%2C6%2C-100%2Cx-8%2C-2x%2B1%29%2C%0D%0A%0D%0Acircle%283%2C-5%2C0.05%29%2Ccircle%283%2C-5%2C0.07%29%2Ccircle%283%2C-5%2C0.09%29%2Ccircle%283%2C-5%2C0.11%29%2Ccircle%283%2C-5%2C0.13%29%2Ccircle%283%2C-5%2C0.15%29%2Ccircle%283%2C-5%2C0.17%29%2Ccircle%283%2C-5%2C0.19%29%2C%0D%0A%0D%0Alocate%283%2B0.3%2C-5%2B0.1%2C%22%283%2C-5%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = x-8 in green<BR>\n" );
document.write( "y = -2x+1 in blue<BR>\n" );
document.write( "The two lines intersect at (3, -5)\r<BR>\n" );
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document.write( "Let's confirm that solution.<BR>\n" );
document.write( "Plug the coordinates into the 1st equation<BR>\n" );
document.write( "y = x-8<BR>\n" );
document.write( "-5 = 3-8<BR>\n" );
document.write( "-5 = -5<BR>\n" );
document.write( "The 1st equation is confirmed.<BR>\n" );
document.write( "Do the same for the 2nd equation<BR>\n" );
document.write( "y = -2x+1<BR>\n" );
document.write( "-5 = -2(3)+1<BR>\n" );
document.write( "-5 = -6+1<BR>\n" );
document.write( "-5 = -5<BR>\n" );
document.write( "Both equations have been confirmed true.\r<BR>\n" );
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document.write( "More practice with graphing a system of linear equations<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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