document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=672213>Question 672213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem states, \"Solve the system of equations using substitution method\".\r<BR>\n" );
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document.write( "This is what I did so far...\r<BR>\n" );
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document.write( "x=3y -- equation 1<BR>\n" );
document.write( "9x - 3y=12 -- equation 2\r<BR>\n" );
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document.write( "Step 1: Substitute x in equation 2 and solve<BR>\n" );
document.write( "9x - 3y=12; x=3y<BR>\n" );
document.write( "9(3y) - 3y=12<BR>\n" );
document.write( "27y - 3y=12<BR>\n" );
document.write( "24y=12<BR>\n" );
document.write( "24y/24=12/24<BR>\n" );
document.write( "y=1/2\r<BR>\n" );
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document.write( "Step 2: Substitute y in equation 1 and solve<BR>\n" );
document.write( "x=3y<BR>\n" );
document.write( "x=3/1(1/2)<BR>\n" );
document.write( "x=3/2\r<BR>\n" );
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document.write( "Now, according to the answer key in my textbook, it states that there is no solution and that the lines are parallel. As you can see above, I somehow came up with a solution of (3/2, 1/2). Substituting (3/2, 1/2) into the original equations made them true (equal), not false (unequal). Please tell me where I went wrong with this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417921 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The problem states, \"Solve the system of equations using substitution method\".\r<BR>\n" );
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document.write( "This is what I did so far...\r<BR>\n" );
document.write( "\n" );
document.write( "x=3y -- equation 1<BR>\n" );
document.write( "9x - 3y=12 -- equation 2\r<BR>\n" );
document.write( "\n" );
document.write( "Step 1: Substitute x in equation 2 and solve<BR>\n" );
document.write( "9x - 3y=12; x=3y<BR>\n" );
document.write( "9(3y) - 3y=12<BR>\n" );
document.write( "27y - 3y=12<BR>\n" );
document.write( "24y=12<BR>\n" );
document.write( "24y/24=12/24<BR>\n" );
document.write( "y=1/2\r<BR>\n" );
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document.write( "Step 2: Substitute y in equation 1 and solve<BR>\n" );
document.write( "x=3y<BR>\n" );
document.write( "x=3/1(1/2)<BR>\n" );
document.write( "x=3/2\r<BR>\n" );
document.write( "\n" );
document.write( "Now, according to the answer key in my textbook, it states that there is no solution and that the lines are parallel. As you can see above, I somehow came up with a solution of (3/2, 1/2). Substituting (3/2, 1/2) into the original equations made them true (equal), not false (unequal). Please tell me where I went wrong with this problem.\r<BR>\n" );
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document.write( "x = 3y ---- eq (i)<BR>\n" );
document.write( "9x – 3y = 12 ---- 3(3x – y) = 3(4) ------- 3x – y = 4 ------ eq (ii)<BR>\n" );
document.write( "3(3y) – y = 4 ------ Substituting 3y for x in eq (ii)<BR>\n" );
document.write( "9y – y = 4<BR>\n" );
document.write( "8y = 4\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F8 ALIGN=MIDDLE  ALT=\"4%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y+=+1%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y+=+1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%281%2F2%29 ALIGN=MIDDLE  ALT=\"x+=+3%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Substituting ˝ for y in eq (i)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x+=+1%261%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x+=+1%261%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%283%2F2%29_%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%283%2F2%29_%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Your solution is correct!!\r<BR>\n" );
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document.write( "The answer you described, from the book, is INCORRECT, as the lines formed from the equations are NOT PARALLEL. Are you certain you’re looking at the right answer? When put in slope-intercept form, as seen below, the slopes are NOT EQUAL, thereby NOT PARALLEL, and thereby having a solution.\r<BR>\n" );
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document.write( "x = 3y ---- 3y = x ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2F3 ALIGN=MIDDLE  ALT=\"y+=+x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F3%29x ALIGN=MIDDLE  ALT=\"y+=+%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Slope, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1%2F3 ALIGN=MIDDLE  ALT=\"m+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "9x - 3y = 12 ---- 3(3x – y) = 3(4) --- 3x – y = 4 --- - y = - 3x + 4 --- y = 3x – 4 --- Slope, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+3 ALIGN=MIDDLE  ALT=\"m+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As seen above, the slopes are DIFFERENT\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
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