document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615001>Question 615001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please help in showing me the steps to solve this equation?  thank you.\r<BR>\n" );
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document.write( "The point (6, 2) lies on the line -x – 8y = -22. Determine if this point is a solution of the system \r<BR>\n" );
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document.write( "-x – 8y = -22<BR>\n" );
document.write( "-7x + 3y = -36 <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #386858 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=386858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the point is (6,2)<BR>\n" );
document.write( "it lies on the line:<BR>\n" );
document.write( "-x - 8y = -22.<BR>\n" );
document.write( "if it was a solution to the system of linear equations, then the point would be at the intersection of the 2 lines of those equations.<BR>\n" );
document.write( "if it was at the intersection of those 2 lines, it would be common to both lines.<BR>\n" );
document.write( "it would therefore have to be on both lines.<BR>\n" );
document.write( "if it was on both lines, then both equations would be true when you replaced x and y with 6 and 2.<BR>\n" );
document.write( "let's see what happens if we do that.<BR>\n" );
document.write( "first equation is -x - 8y = -22<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "-(6) - 8(2) = -6 - 16 = -22<BR>\n" );
document.write( "it is definitely on the first line.<BR>\n" );
document.write( "second equation is -7x + 3y = -36<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "-7(6) + 3(2) = -42 + 6 = -36<BR>\n" );
document.write( "looks like it's on the second line too.<BR>\n" );
document.write( "since the point is common to both equations, it is a simultaneous solution of the system of those equations<BR>\n" );
document.write( "you can graph these equations as shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%28-22%2Bx%29%2F-8%2C%287x-36%29%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%28-22%2Bx%29%2F-8%2C%287x-36%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that the lines intersect at the point (6,2).\r<BR>\n" );
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