document.write( "Question 1045058: Which of the following ordered pairs satisfy both 3x - y < 10 and x + 6y > 15?
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Algebra.Com's Answer #660464 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Which of the following ordered pairs satisfy both 3x - y < 10 and x + 6y > 15?
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document.write( "Plug 'em in and see:\r\n" );
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document.write( "A. Plug in (x,y) = (-3,-3)\r\n" );
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document.write( "Plug it in the first inequality: \r\n" );
document.write( "      3x - y < 10\r\n" );
document.write( "3(-3) - (-3) < 10\r\n" );
document.write( "      -9 + 3 < 10\r\n" );
document.write( "          -6 < 10\r\n" );
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document.write( "That's true.\r\n" );
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document.write( "Plug it in the second inequality:\r\n" );
document.write( "      x + 6y > 15\r\n" );
document.write( "(-3) + 6(-3) > 15\r\n" );
document.write( "     -3 - 18 > 15\r\n" );
document.write( "         -21 > 15\r\n" );
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document.write( "That's false.  So A isn't the answer because, even\r\n" );
document.write( "though the first inequality is true, the seconds one\r\n" );
document.write( "isn't, and in the correct choice, BOTH must be true.\r\n" );
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document.write( "B. Plug in (x,y) = (9,1)\r\n" );
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document.write( "Plug it in the first inequality: \r\n" );
document.write( "      3x - y < 10\r\n" );
document.write( "  3(9) - (1) < 10\r\n" );
document.write( "      27 - 1 < 10\r\n" );
document.write( "          26 < 10\r\n" );
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document.write( "That's false.  So there is no use to plug it in \r\n" );
document.write( "the second inequality for even if it would be \r\n" );
document.write( "true if we substituted it in the second inequality, \r\n" );
document.write( "it would not be the correct choice because it \r\n" );
document.write( "must give a true inequality when substituted \r\n" );
document.write( "in EITHER one!\r\n" );
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document.write( "C. Plug in (x,y) = (-6,6)\r\n" );
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document.write( "Plug it in the first inequality: \r\n" );
document.write( "      3x - y < 10\r\n" );
document.write( " 3(-6) - (6) < 10\r\n" );
document.write( "     -18 + 6 < 10\r\n" );
document.write( "          -6 < 10\r\n" );
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document.write( "That's true.\r\n" );
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document.write( "Plug it in the second inequality:\r\n" );
document.write( "      x + 6y > 15\r\n" );
document.write( " (-6) + 6(6) > 15\r\n" );
document.write( "     -6 + 36 > 15\r\n" );
document.write( "          30 > 15\r\n" );
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document.write( "That's true.  So C is a correct answer.\r\n" );
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document.write( "The problem just states\r\n" );
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document.write( "\"Which of the following ordered pairs satisfy both 3x - y < 10 \r\n" );
document.write( "and x + 6y > 15?\"\r\n" );
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document.write( "It doesn't say \r\n" );
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document.write( "Which ONE of the following ordered pairs satisfy both 3x - y < 10 \r\n" );
document.write( "and x + 6y > 15? \r\n" );
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document.write( "So we have to see if D is also a correct answer as well:\r\n" );
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document.write( "D. Plug in (x,y) = (7,-4)\r\n" );
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document.write( "Plug it in the first inequality: \r\n" );
document.write( "      3x - y < 10\r\n" );
document.write( " 3(7) - (-4) < 10\r\n" );
document.write( "      21 + 4 < 10\r\n" );
document.write( "          25 < 10\r\n" );
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document.write( "That's false.   So now we know that there is only one\r\n" );
document.write( "answer that is correct, and that is C.\r\n" );
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document.write( "Edwin

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