document.write( "Question 1120283: x −2y ≥ 0, 2x−y ≤−2, x≥0,y ≥0 solve graphically \n" ); document.write( "

Algebra.Com's Answer #735971 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The given system of inequalities is equivalent to \r\n" );
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document.write( "    y <=                (1)\r\n" );
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document.write( "    y >= 2x + 2           (2)\r\n" );
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document.write( "    x >= 0,  y >= 0       (3)\r\n" );
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document.write( "The plot below represents line (1) in red and line (2) in green.\r\n" );
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document.write( "Plot y =  (red) and y = 2x+2 (green).\r\n" );
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document.write( "The solution to inequality (1) is the set of all points belonging to the half plane on and below the red line (including points of this line).\r\n" );
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document.write( "The solution to inequality (2) is the set of all points belonging to the half plane on and  above the green line (including points of this line).\r\n" );
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document.write( "The solution to inequality (3) is the set of all points belonging to first quadrant QI (including points of x- and y-axes).\r\n" );
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document.write( "The solution to the given system of inequalities (1), (2) and (3) is the intersection of the sets described above.\r\n" );
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document.write( "As you can see it from the plot, this intersection is the EMPTY set  (which means that there is no point  (x,y)  \r\n" );
document.write( "in the coordinate plane satisfying given inequalities simultaneously).\r\n" );
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document.write( "Thus the set of solution to the given system is the empty set.\r\n" );
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document.write( "In other words, the given system HAS NO solutions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be aware : the solution and the answer by @Boreal is I N C O R R E C T. \r
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