document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109909>Question 109909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help PLEASE!!!! <BR>\n" );
document.write( "solve each of the following by substitution \r<BR>\n" );
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document.write( "4x-12y=5<BR>\n" );
document.write( "-x+3y=-1\r<BR>\n" );
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document.write( "Thanks<BR>\n" );
document.write( "Heather </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80093 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=80093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x-12y=5-------------------------eq1<BR>\n" );
document.write( "-x+3y=-1 -------------------------eq2\r<BR>\n" );
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document.write( "O.K. now we will solve for x in eq2 and substitute the value for x into eq1:\r<BR>\n" );
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document.write( "-x+3y=-1  subtract 3y from both sides\r<BR>\n" );
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document.write( "-x+3y-3y=-1-3y  collect like terms\r<BR>\n" );
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document.write( "-x=-1-3y  multiply each term by -1\r<BR>\n" );
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document.write( "x=1+3y--------------------Now we will substitute this into eq1 and we get:\r<BR>\n" );
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document.write( "4(1+3y)-12y=5  get rid of parens (distributive law)<BR>\n" );
document.write( "4+12y-12y=5--------------------WHOAA!!!!!!! SOMETHING IS WRONG.  THERE'S NO SOLUTION \r<BR>\n" );
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document.write( "Lets put eq1 into slope-intercept form  (y=mx+b where m is the slope and b is the y-intercept, remember?)\r<BR>\n" );
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document.write( "4x-12y=5 subtract 4x from both sides\r<BR>\n" );
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document.write( "4x-4x-12y=5-4x  collect like terms\r<BR>\n" );
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document.write( "-12y=-4x+5  divide each term by -12<BR>\n" );
document.write( "y=(4/12)x-5/12 or<BR>\n" );
document.write( "y=(1/3)x-5/12   ----------------------eq1 in slope-intercept form<BR>\n" );
document.write( "Slope of eq1 is 1/3\r<BR>\n" );
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document.write( "Now for eq2:\r<BR>\n" );
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document.write( "-x+3y=-1 add x to both sides<BR>\n" );
document.write( "-x+x+3y=-1+x  collect like terms<BR>\n" );
document.write( "3y=x-1  divide each term by 3<BR>\n" );
document.write( "y=(1/3)x-1/3----------------------eq2 in slope-intercept\r<BR>\n" );
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document.write( "Slope of eq2 is 1/3\r<BR>\n" );
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document.write( "The two lines are parallel.  The equations are inconsistent---there is no solution\r<BR>\n" );
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document.write( "Hope this helps----ptaylor<BR>\n" );
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