Since y=(2x−3)(x+9) and x=2y+5, it follows that x=2((2x−3)(x+9))+5=4x2+30x−54. This can be rewritten as 4x2+29x−54=0 Because the discriminant of this quadratic equation,292−(4)(−54)=292+4(54), is positive, this equation has 2 distinct roots. Using each of the roots as the value of x and finding y from the equation x=2y+5 gives 2 ordered pairs (x,y) that satisfy the given system of equations. Since no other value of x satisfies 4x2+29x−54=0, there are no other ordered pairs that satisfy the given system. Therefore, there are 2 ordered pairs (x,y) that satisfy the given system of equations. Choices A and B are incorrect and may be the result of either a miscalculation or a conceptual error. Choice D is incorrect because a system of one quadratic equation and one linear equation cannot have infinitely many solutions.