document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58649>Question 58649</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321369580/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the systems of equations graphically<BR>\n" );
document.write( "{4x-3y=-4<BR>\n" );
document.write( "{2x-5y=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40266 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=40266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to solve this graphically we have to plot the graphs.<BR>\n" );
document.write( "Arrange the equation in the \"y=\" format\r<BR>\n" );
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document.write( "4x - 3y = -4<BR>\n" );
document.write( "-3y = -4 - 4x<BR>\n" );
document.write( "3y = 4x + 4, multiplied equation by -1, y should be positive<BR>\n" );
document.write( "y = (4/3)x + (4/3)<BR>\n" );
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document.write( "Find the value of y by substituting for x:<BR>\n" );
document.write( " x |   y<BR>\n" );
document.write( "-2 | -(4/3)<BR>\n" );
document.write( "-1 | 0<BR>\n" );
document.write( "0  | +(4/3)<BR>\n" );
document.write( "+1 | +(8/3)<BR>\n" );
document.write( "+2 | +4<BR>\n" );
document.write( "Plot these on a graph: x axis 4/-4 and y axis 4/-4 will work ok<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Do the same with the 2nd equation:\r<BR>\n" );
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document.write( "2x-5y=-4<BR>\n" );
document.write( "-5y = -4 - 2x<BR>\n" );
document.write( "5y = 2x + 4<BR>\n" );
document.write( "y = (2/5)x + (4/5)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the value of y by substituting for x:<BR>\n" );
document.write( " x |   y<BR>\n" );
document.write( "-2 | 0<BR>\n" );
document.write( "-1 | +(2/5)<BR>\n" );
document.write( "0  | +(4/5)<BR>\n" );
document.write( "+1 | +(6/5)<BR>\n" );
document.write( "+2 | +(8/5)<BR>\n" );
document.write( "Plot this on the same graph, it should look like this(green is 2nd equation):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+4%2C+%284%2F3%29x+%2B+%284%2F3%29%2C+%282%2F5%29x+%2B+%284%2F5%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The solution is the x,y values where the lines cross. YOu can see it is not<BR>\n" );
document.write( "going to be an integer. I solved using elimination, got x = -(4/7) y = +(4/7)<BR>\n" );
document.write( "which looks about right<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );