Find the ordered pair that is a solution to the graphs\r
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document.write( "a) (3,7)
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document.write( "We substitute the first number of the ordered pair, which is 3,\r\n" );
document.write( "in place of x and the second number, which is 7, in place of y \r\n" );
document.write( "in both equations and simplify. \r\n" );
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document.write( "Substituting 3 for x, and 7 for y in the first one:\r\n" );
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document.write( "That's a false equation because 7 does not equal 9.\r\n" );
document.write( "So the ordered paie (3.7) is not a solution to .\r\n" );
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document.write( "Substituting 3 for x, and 7 for y in the second one:\r\n" );
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document.write( "That's a false equation because 7 does not equal 1.\r\n" );
document.write( "So the ordered paie (3.7) is not a solution to the\r\n" );
document.write( "equation .\r\n" );
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document.write( "So the ordered pair (3,7) is not a solution to\r\n" );
document.write( " because it is not a solution\r\n" );
document.write( "to either one of the equations, so it cannot be a solution\r\n" );
document.write( "to both.\r\n" );
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document.write( "If what we had ended up with in BOTH cases had been true equations,\r\n" );
document.write( "then the ordered pair would have been a solution. But in this \r\n" );
document.write( "case they were both false, so the ordered pair (3,7) is not a \r\n" );
document.write( "solution to . \r\n" );
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document.write( "b) (0,7)
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document.write( "We substitute the first number of the ordered pair, which is 0,\r\n" );
document.write( "in place of x and the second number, which is 7, in place of y \r\n" );
document.write( "in both equations and simplify. \r\n" );
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document.write( "Substituting 0 for x, and 7 for y in the first one:\r\n" );
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document.write( "That's a false equation because 7 does not equal 3.\r\n" );
document.write( "So the ordered paie (0.7) is not a solution to .\r\n" );
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document.write( "Substituting 0 for x, and 7 for y in the second one:\r\n" );
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document.write( "That's a false equation because 7 does not equal 1.\r\n" );
document.write( "So the ordered paie (3.7) is not a solution to the\r\n" );
document.write( "equation .\r\n" );
document.write( " \r\n" );
document.write( "So the ordered pair (3,7) is not a solution to\r\n" );
document.write( " because it is not a solution\r\n" );
document.write( "to either one of the equations, so it cannot be a solution\r\n" );
document.write( "to both.\r\n" );
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document.write( "If what we had ended up with in BOTH cases had been true equations,\r\n" );
document.write( "then the ordered pair would have been a solution. But in this \r\n" );
document.write( "case they were both false, so the ordered pair (0,7) is not a \r\n" );
document.write( "solution to . \r\n" );
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document.write( "c) (7,2)
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document.write( "We substitute the first number of the ordered pair, which is 7,\r\n" );
document.write( "in place of x and the second number, which is 2, in place of y \r\n" );
document.write( "in both equations and simplify. \r\n" );
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document.write( "Substituting 7 for x, and 2 for y in the first one:\r\n" );
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document.write( "That's a false equation because 2 does not equal 17.\r\n" );
document.write( "So the ordered paie (7.2) is not a solution to .\r\n" );
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document.write( "Substituting 7 for x, and 2 for y in the second one:\r\n" );
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document.write( "That's a false equation because 2 does not equal 5.\r\n" );
document.write( "So the ordered paie (7.2) is not a solution to the\r\n" );
document.write( "equation .\r\n" );
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document.write( "So the ordered pair (7,2) is not a solution to\r\n" );
document.write( " because it is not a solution\r\n" );
document.write( "to either one of the equations, so it cannot be a solution\r\n" );
document.write( "to both.\r\n" );
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document.write( "If what we had ended up with in BOTH cases had been true equations,\r\n" );
document.write( "then the ordered pair would have been a solution. But in this \r\n" );
document.write( "case they were both false, so the ordered pair (7,2) is not a \r\n" );
document.write( "solution to .\r\n" );
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document.write( "d) (-5, -7)
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document.write( "We substitute the first number of the ordered pair, which is -5,\r\n" );
document.write( "in place of x and the second number, which is -7, in place of y \r\n" );
document.write( "in both equations and simplify. \r\n" );
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document.write( "Substituting -5 for x, and -7 for y in the first one:\r\n" );
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document.write( "That's a true equation because -7 does equal -7.\r\n" );
document.write( "So the ordered paie (-5.-7) is a solution to .\r\n" );
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document.write( "Substituting -5 for x, and -7 for y in the second one:\r\n" );
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document.write( "That's a true equation because -7 does equal -7.\r\n" );
document.write( "So the ordered paie (3.7) is a solution to the\r\n" );
document.write( "equation .\r\n" );
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document.write( "So the ordered pair (3,7) is a solution to\r\n" );
document.write( " because it is a solution\r\n" );
document.write( "to BOTH of the equations.\r\n" );
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document.write( "So the correct choice is (d).\r\n" );
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document.write( "The significance of this is that if we graph both lines,\r\n" );
document.write( "by plotting points, we get this.\r\n" );
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document.write( "We see that the point that is on both lines is the point\r\n" );
document.write( "whose set of coordinates is the ordered pair (-5,-7), the\r\n" );
document.write( "point where the two lines cross. That's because if you draw\r\n" );
document.write( "a green vertical line and a green horizontal line through \r\n" );
document.write( "the point where the two red lines cross, like this:\r\n" );
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document.write( "that the vertical line crosses the x-axis at -5 and the\r\n" );
document.write( "horizontal line crosses the y-axis at -7. \r\n" );
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document.write( "Edwin
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