document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35125>Question 35125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the intercept point of y=3x+8 and 4x+2y=6.  If you can find the answer, would you explain it to me?  I also have a few more to do and I need to understand how to do it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21338 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=21338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> each is just a straight line, so if they cross, will be equal at that one point...the solution.\r<BR>\n" );
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document.write( "As to how to do it: at that one point, the x,y values in both equation are the same eg at x=2, then y will be whatever, but both equations will give the same answer...the point is the same on both lines.\r<BR>\n" );
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document.write( "OK, i have laboured the point enough. Method:<BR>\n" );
document.write( "y=3x+8 and 4x+2y=6<BR>\n" );
document.write( "--> 2y=6x+16 is the first equation scalled up by factor of 2. Why did i do that? Well, now both equations have a \"2y\" term, so i can put one version into the other equation and just have an equation in \"x\", so i can solve that:\r<BR>\n" );
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document.write( "sub 6x+16 in place of 2y in 4x+2y=6\r<BR>\n" );
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document.write( "--> 4x+(6x+16)=6<BR>\n" );
document.write( "4x+6x+16=6<BR>\n" );
document.write( "10x+16=6<BR>\n" );
document.write( "10x=-10<BR>\n" );
document.write( "x=-10/10<BR>\n" );
document.write( "--> x=-1\r<BR>\n" );
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document.write( "and so from y=3x+8 (or the other one, it doesn't matter: i just picked the simplest one to work with) and knowing that x=-1, we get\r<BR>\n" );
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document.write( "y=3(-1)+8<BR>\n" );
document.write( "y=-3+8<BR>\n" );
document.write( "y=5\r<BR>\n" );
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document.write( "So the solution is x=-1, y=5\r<BR>\n" );
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document.write( "CHECK other equation:<BR>\n" );
document.write( "4x+2y=6<BR>\n" );
document.write( "4(-1)+2(5)<BR>\n" );
document.write( "-4+10<BR>\n" );
document.write( "6 --> which is what the equation does equal, so we KNOW we have the correct answer.\r<BR>\n" );
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document.write( "Move on to next question, happy that you KNOW it is correct :-)\r<BR>\n" );
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document.write( "jon. </SPAN>\n" );
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