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Test
Math
Domain
Algebra
Skill
Linear inequalities in one or two variables
Difficulty
Hard
ID: 541bef2f
Modded SAT Question Bank by Abdullah Mallik

yx+7

y-2x-1

Which point x,y is a solution to the given system of inequalities in the xy-plane?

  1. -14,0

  2. 0,-14

  3. 0,14

  4. 14,0


Tip: Press CTRL/Command to toggle answer
Correct Answer: D
Rationale

Choice D is correct. A point x,y is a solution to a system of inequalities in the xy-plane if substituting the x-coordinate and the y-coordinate of the point for x and y, respectively, in each inequality makes both of the inequalities true. Substituting the x-coordinate and the y-coordinate of choice D, 14 and 0, for x and y, respectively, in the first inequality in the given system, yx+7, yields 014+7, or 021, which is true. Substituting 14 for x and 0 for y in the second inequality in the given system, y-2x-1, yields 0-214-1, or 0-29, which is true. Therefore, the point 14,0 is a solution to the given system of inequalities in the xy-plane.

Choice A is incorrect. Substituting -14 for x and 0 for y in the inequality yx+7 yields 0-14+7, or 0-7, which is not true.

Choice B is incorrect. Substituting 0 for x and -14 for y in the inequality y-2x-1 yields -14-20-1, or -14-1, which is not true.

Choice C is incorrect. Substituting 0 for x and 14 for y in the inequality yx+7 yields 140+7, or 147, which is not true.

Question Difficulty: Hard
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