sat-dog

Choice D is correct. A system of two linear equations in two variables, x and y, has no solution if the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by + = equations in the form Ax By C, where A, B, and C are constants, are parallel if the coefficients for x and y in one equation are proportional to the corresponding coefficients in the other equation. The first equation in the given + = system can be written in the form Ax By C by subtracting 9y from both sides 4 -18 =5 of the equation to yield x y . The second equation in the given system + = can be written in the form Ax By C by subtracting 4x from both sides of the -4 + =2 - equation to yield x hy . The coefficient of x in this second equation, 4, - is 1 times the coefficient of x in the first equation, 4. For the lines to be parallel, - the coefficient of y in the second equation, h, must also be 1 times the -18 =-1 -18 =18 coefficient of y in the first equation, . Thus, h ^ h, or h . 18 Therefore, if the given system has no solution, the value of h is . - Choice A is incorrect. If the value of h is 9, then the given system would have one solution, rather than no solution. Choice B is incorrect. If the value of h is 0, then the given system would have one solution, rather than no solution. Choice C is incorrect. If the value of h is 9, then the given system would have one solution, rather than no solution.