document.write( "Question 56261: Here it is again! I know how to do this, I just don't have the resourse, can someone help me to graph this problem
\n" ); document.write( "x-y<3
\n" ); document.write( "x+2y>6\r
\n" ); document.write( "\n" ); document.write( "another problem that I have is, solve the system by addition or substitution.
\n" ); document.write( "3x+6y=0
\n" ); document.write( " x=2/3 how in the world do I go about even solving this!?!? \n" ); document.write( "
Algebra.Com's Answer #38167 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Here it is again! I know how to do his,I just don't have the \r\n" );
document.write( "resourse, can someone help me to graph this problem.\r\n" );
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document.write( "x -  y < 3\r\n" );
document.write( "x + 2y > 6\r\n" );
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document.write( "This is the graph of a shaded region\r\n" );
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document.write( "First draw the graphs of the boundary lines.  \r\n" );
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document.write( "Boundary line's equations:  |  Boundary line's intercepts\r\n" );
document.write( "                            | \r\n" );
document.write( "       x -  y = 3           |    (0,-3)         (3,0)   \r\n" );
document.write( "       x + 2y = 6           |     (0,3)         (6,0) \r\n" );
document.write( "                            |\r\n" );
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document.write( "Just draw one boundary line at a time so you can tell\r\n" );
document.write( "which area to shade.\r\n" );
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document.write( "Draw the first bondary line by plotting its two intercepts\r\n" );
document.write( "and drawing a dotted line thru them.  Draw it dotted since\r\n" );
document.write( "it is strictly less than.  I can only draw it solid on here,\r\n" );
document.write( "but you can draw it dotted on your paper:\r\n" );
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document.write( "\"+graph%28+300%2C+300%2C+-9%2C+9%2C+-9%2C+9%2C+x-3%29+\"\r\n" );
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document.write( "Now before drawing the other boundary line, we must decide which\r\n" );
document.write( "side of this line we will shad on.\r\n" );
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document.write( "To do this we pick any point which is not on that line as a test\r\n" );
document.write( "point, say, we pick (3,2) for we can be sure that is not on the\r\n" );
document.write( "line.  We substitute x=3 and y=2 into the inequality\r\n" );
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document.write( "x - y < 3\r\n" );
document.write( "3 - 2 < 3\r\n" );
document.write( "    1 < 3\r\n" );
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document.write( "That is a true inequality, since 1 really is less than 3, so we \r\n" );
document.write( "know to shade the side of the boundary line that the test point \r\n" );
document.write( "(3,2) is on.  That's the side above the line. [BTW if that\r\n" );
document.write( "inequality had come out false, then we'd have known to shade the\r\n" );
document.write( "other side, the lower side. instead.]\r\n" );
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document.write( "Now draw the second boundary line by plotting its two intercepts\r\n" );
document.write( "and drawing a dotted line thru them.  Draw it dotted also since\r\n" );
document.write( "it is strictly greater than.  I can only draw it solid on here,\r\n" );
document.write( "but you can draw it dotted on your paper:\r\n" );
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document.write( "\"+graph%28+300%2C+300%2C+-9%2C+9%2C+-9%2C+9%2C+x-3%2C+%286-x%29%2F2%29+\"\r\n" );
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document.write( "Now we must also decide which side of this line we will shade.\r\n" );
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document.write( "As before, to do this we pick any point which is not on that line \r\n" );
document.write( "as a test point, say, we pick (2,1) for we can be sure that is not \r\n" );
document.write( "on the green line.  We substitute x=2 and y=1 into the inequality\r\n" );
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document.write( "  x + 2y > 6\r\n" );
document.write( "2 + 2(1) > 5\r\n" );
document.write( "       4 > 5\r\n" );
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document.write( "That is a false inequality, since 4 is NOT greater than 5, so we \r\n" );
document.write( "know to shade the side of the boundary line that the test point \r\n" );
document.write( "(2,1) is NOT on.  That's the side above the green line.    \r\n" );
document.write( " \r\n" );
document.write( "So the section we shade is the V-shaped region which is above\r\n" );
document.write( "both the red and the green lines.  And the lines are supposed\r\n" );
document.write( "to be drawn dotten, not solid.  [You would have drawn them\r\n" );
document.write( "solid if the inequalities had been < or >.]\r\n" );
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document.write( "another problem that I have is, solve the system by addition or \r\n" );
document.write( "substitution.\r\n" );
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document.write( "3x + 6y = 0\r\n" );
document.write( "      x = 2/3 \r\n" );
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document.write( "Since the second equation already gives you the value for x,\r\n" );
document.write( "namely 2/3, the problem is half-worked for you from the start.\r\n" );
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document.write( "So all you have to do is finish by substituting 2/3 for x in \r\n" );
document.write( "the first equation and solve for y.\r\n" );
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document.write( "    3x + 6y = 0\r\n" );
document.write( "3(2/3) + 6y = 0     \r\n" );
document.write( "     2 + 6y = 0\r\n" );
document.write( "         6y = -2\r\n" );
document.write( "          y = -2/6\r\n" );
document.write( "          y = -1/3\r\n" );
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document.write( "So the solution is (x,y) = (2/3,-1/3)\r\n" );
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document.write( "Edwin
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