document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=306433>Question 306433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the values of x and y that ensure eace quadrilateral is a parallelogram? The top is 2x-4, the bottom is 10, the left side is -3y and the right side is 12-y. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #219308 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=219308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If each quadrilateral is a parallelogram, then the opposite sides have to be parallel to each other.\r<BR>\n" );
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document.write( "The top is 2x-4<BR>\n" );
document.write( "The bottom is 10<BR>\n" );
document.write( "The left side4 is -3y<BR>\n" );
document.write( "The right side is 12-y.\r<BR>\n" );
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document.write( "?????\r<BR>\n" );
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document.write( "The bottom has to be parallel to the top.<BR>\n" );
document.write( "I have no idea what you mean by the bottom is 10, but let's just say that the bottom is 2x + 10.<BR>\n" );
document.write( "This give it the same slope as the top.\r<BR>\n" );
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document.write( "The left side is -3y and the right side is 12 - y.\r<BR>\n" );
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document.write( "?????\r<BR>\n" );
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document.write( "-3y means y = -1/3\r<BR>\n" );
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document.write( "12 - y means y = 12.\r<BR>\n" );
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document.write( "That's possible since the slope of the equations would both = 0.\r<BR>\n" );
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document.write( "To graph this equation, we would get graph the equations:\r<BR>\n" );
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document.write( "y = 2x-4<BR>\n" );
document.write( "y = 2x - 10<BR>\n" );
document.write( "y = -1/3<BR>\n" );
document.write( "y = 12\r<BR>\n" );
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document.write( "The graph would look like this:\r<BR>\n" );
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document.write( "You can see that we have a parallelogram because the top and bottom sides are parallel to each other, and the left and right sides are also parallel to each other.\r<BR>\n" );
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document.write( "I'm not sure if this is the parallelogram  you were thinking about, but this is a prallelogram.\r<BR>\n" );
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document.write( "The slopes of the opposite sides have to be equal to each other.\r<BR>\n" );
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document.write( "The y intercepts can be anything as long as they are different from each other.\r<BR>\n" );
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document.write( "The equation of a straight line is y = mx + b.\r<BR>\n" );
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document.write( "m is the slope.\r<BR>\n" );
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document.write( "b is the y-intercept which is the value of y when x = 0.\r<BR>\n" );
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document.write( "The equations we just showed on the graph are:\r<BR>\n" );
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document.write( "y = 2x-4<BR>\n" );
document.write( "y = 2x - 10<BR>\n" );
document.write( "y = -1/3<BR>\n" );
document.write( "y = 12\r<BR>\n" );
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document.write( "Another set of equations where the slopes are the same but the y-intercepts are different would be:\r<BR>\n" );
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document.write( "y = 2x-4<BR>\n" );
document.write( "y = 2x+15<BR>\n" );
document.write( "y = -5<BR>\n" );
document.write( "y = 5\r<BR>\n" );
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document.write( "A graph of these equations would look like this:\r<BR>\n" );
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document.write( "The parallelogram is positioned in a different spot, but it is still a parallelogram and the parallel sides are still oriented in the same direction.\r<BR>\n" );
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document.write( "This is because the y-intercepts have changed, but the slopes have remained the same.\r<BR>\n" );
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document.write( "The parallelograms we are talking about are the spaces that are bounded by the parallel lines.\r<BR>\n" );
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document.write( "The corner point of the parallelograms would be the intersections of the 2 sets of parallel lines.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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