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Test
Math
Domain
Algebra
Skill
Systems of two linear equations in two variables
Difficulty
Hard
ID: 14360f84
Modded SAT Question Bank by Abdullah Mallik

4x-9y=9y+5

hy=2+4x

In the given system of equations, h is a constant. If the system has no solution, what is the value of h?

  1. -9

  2. 0

  3. 9

  4. 18


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Correct Answer: D
Rationale

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 of the equation to yield 4x-18y=5. The second equation in the given system can be written in the form Ax+By=C by subtracting 4x from both sides of the equation to yield -4x+hy=2. 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 coefficient of y in the first equation, -18. Thus, h=-1(-18), or h=18. Therefore, if the given system has no solution, the value of h is 18.

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.

Question Difficulty: Hard
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