\r\n" );
document.write( "The other tutors were no help. You are supposed to do it by graphing,\r\n" );
document.write( "not by elimination, as the first one suggests. The second tutor tried\r\n" );
document.write( "to do it that way, but his answer is wrong. Here's how to do it by \r\n" );
document.write( "graphing.\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Find three points on the first line:\r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|\r\n" );
document.write( " |2\r\n" );
document.write( "-8|\r\n" );
document.write( "\r\n" );
document.write( " 2x-y = -8 2x-y = -8 2x-y = -8\r\n" );
document.write( "2(0)-y = -8 2x-2 = -8 2(-8)-y = -8 \r\n" );
document.write( " 0-y = -8 2x = -6 -16-y = -8\r\n" );
document.write( " -y = -8 x = -3 -y = 8\r\n" );
document.write( " y = 8 y = -8\r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|8\r\n" );
document.write( "-3|2\r\n" );
document.write( "-8|-8\r\n" );
document.write( "\r\n" );
document.write( "Plot them and draw a line through them.\r\n" );
document.write( "\r\n" );
document.write( "You have to be accurate, so use graph paper and a ruler or straight edge.\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "---------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Find three points on the second line:\r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|\r\n" );
document.write( " |2\r\n" );
document.write( "-8|\r\n" );
document.write( "\r\n" );
document.write( " -3x+2y = 10 -3x+2y = 10 -3x+2y = 10\r\n" );
document.write( "-3(0)+2y = 10 -3x+2(2) = 10 -3(-8)+2y = 10 \r\n" );
document.write( " 2y = 10 -3x+4 = 10 24+2y = 10\r\n" );
document.write( " y = 5 -3x = 6 2y = -14\r\n" );
document.write( " x = -2 y = -7\r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|5\r\n" );
document.write( "-2|2\r\n" );
document.write( "-8|-7\r\n" );
document.write( "\r\n" );
document.write( "Plot them and draw a line through them:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Notice the point where the two lines cross (intersect). I'll make it red.\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "From that point where the two lines intersect, draw one vertical line directly\r\n" );
document.write( "to the x-axis and draw another horizontal line directly to the y-axis. I'll\r\n" );
document.write( "draw those in green:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "So the value of x is x=-6, since one green line touches the x-axis at -6\r\n" );
document.write( "and the value of y is y=-4, since the other green line touches the y-axis at -4.\r\n" );
document.write( "\r\n" );
document.write( "So the answer is (x,y) = (-6,-4)\r\n" );
document.write( "\r\n" );
document.write( "Check by substituting:\r\n" );
document.write( "\r\n" );
document.write( " 2x-y = -8 -3x+2y = 10 \r\n" );
document.write( " 2(-6)-(-4) = -8 -3(-6)+2(-4) = 10\r\n" );
document.write( " -12+4 = -8 18-8 = 10\r\n" );
document.write( " -8 = -8 10 = 10\r\n" );
document.write( "\r\n" );
document.write( "The solution (x,y) = (-6,-4) is correct.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
