document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38010>Question 38010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve graphically ans algebraically:<BR>\n" );
document.write( "-2x+3y=6<BR>\n" );
document.write( " 3x+y=2<BR>\n" );
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document.write( "         write the equation for a solutionline that has points (4,1) and (-2,4)<BR>\n" );
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document.write( "what ordered pair is the y-intercept and the x-intercept of the linear equation 2x+3y=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23561 by </B><A HREF=/tutors/aboutme.mpl?userid=lyra><B>lyra(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lyra><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=lyra><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=23561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please only put ONE question in each submission!!!  I will answer your first question.\r<BR>\n" );
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document.write( "By algebra:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++-2%5Cx+%2B+3%5Cy+=+6%2C%0D%0A++++3%5Cx+%2B+1%5Cy+=+2+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++-2%5Cx+%2B+3%5Cy+=+6%2C%0D%0A++++3%5Cx+%2B+1%5Cy+=+2+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 3*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Ax+=+6+-+3%2Ay ALIGN=MIDDLE  ALT=\"-2%2Ax+=+6+-+3%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2F-2+-+3%2Ay%2F-2 ALIGN=MIDDLE  ALT=\"x+=+6%2F-2+-+3%2Ay%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%286%2F-2+-+3%2Ay%2F-2%29+%2B+1%5Cy+=+2 ALIGN=MIDDLE  ALT=\"3%2A%286%2F-2+-+3%2Ay%2F-2%29+%2B+1%5Cy+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=2. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2F-2+-+3%2Ay%2F-2 ALIGN=MIDDLE  ALT=\"x+=+6%2F-2+-+3%2Ay%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=0.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=0%2C+y=2+%29 ALIGN=MIDDLE  ALT=\"system%28+x=0%2C+y=2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "By graphing<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+x+%2B+3+y+=+6 ALIGN=MIDDLE  ALT=\"-2+x+%2B+3+y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+--2%2F3 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 6/-2 = -3.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/3 = 2.</LI><LI>Slope is --2/3 = 0.666666666666667.</LI><LI> Equation in slope-intercept form: y=0.666666666666667*x+2.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+2-8%2C+2%2B8%2C+0.666666666666667%2Ax%2B2+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-3-8%2C+-3%2B8%2C+2-8%2C+2%2B8%2C+0.666666666666667%2Ax%2B2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+x+%2B+1+y+=+2 ALIGN=MIDDLE  ALT=\"3+x+%2B+1+y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-3%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 2/3 = 0.666666666666667.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 2/1 = 2.</LI><LI>Slope is -3/1 = -3.</LI><LI> Equation in slope-intercept form: y=-3*x+2.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+0.666666666666667-8%2C+0.666666666666667%2B8%2C+2-8%2C+2%2B8%2C+-3%2Ax%2B2+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "Hope this helps and feel free to contact me with further questions,<BR>\n" );
document.write( "lyra\r<BR>\n" );
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