document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971646>Question 971646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the approximate solution of this system of equations.\r<BR>\n" );
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document.write( "y = |x^2 &#8722; 3x + 1|<BR>\n" );
document.write( "y = x &#8722; 1\r<BR>\n" );
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document.write( "a. (1, 0)<BR>\n" );
document.write( "b. (4.5, 3.5)<BR>\n" );
document.write( "c. (2, 1)<BR>\n" );
document.write( "d. (3.4, 2.3)<BR>\n" );
document.write( "e. (0.6, -0.4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594078 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=594078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The absolute value equation has two critical values for x, the roots.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B-+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%283%2B-+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; to the left and right of the roots the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-3x%2B1 ALIGN=MIDDLE  ALT=\"y=x%5E2-3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and between them is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2%2B3x-1 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You just want to find in which interval of x does the line y=x-1 intersect the absolute value equation.\r<BR>\n" );
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document.write( "Try testing for the middle interval first.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=x-1%2Cy=-x%5E2%2B3x-1%29 ALIGN=MIDDLE  ALT=\"system%28y=x-1%2Cy=-x%5E2%2B3x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=-x%5E2%2B3x-1 ALIGN=MIDDLE  ALT=\"x-1=-x%5E2%2B3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "**<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B3x-x=0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B3x-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2Bx=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2Bx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=0 or x=1/2<BR>\n" );
document.write( "(**this must be a mistake.)<BR>\n" );
document.write( "Where is each of these two solutions?  To left of the smaller critical value?  To the right of the greater critical value?  Between the two critical values?\r<BR>\n" );
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document.write( "Solution to the problem not finished, but you should understand this strategy.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C3%2C-3%2C3%2Cx-1%2Cabs%28x%5E2-3x%2B1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C3%2C-3%2C3%2Cx-1%2Cabs%28x%5E2-3x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Once the mistake is corrected, you should find as shown in the graph, the solution is point  (2,1). </SPAN>\n" );
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