SAT Exam > SAT Questions > y < 3x +1x - y >1Which of the following...
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y < 3x +1
x - y >1
Which of the following ordered pairs (x, y) satisfies the system of inequalities above?
x - y >1
Which of the following ordered pairs (x, y) satisfies the system of inequalities above?
- a)(−2, −1)
- b)(−1, 3)
- c)(1, 5)
- d)(2, −1)
Correct answer is option 'D'. Can you explain this answer?
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y < 3x +1x - y >1Which of the following ordered pairs (x, y) sat...
Any point (x, y) that is a solution to the given system of inequalities must satisfy both inequalities in the system. Since the second inequality in the system can be rewritten as y < x - 1, the system is equivalent to the following system.
y < 3x +1
y < x-1
Since 3x + 1 > x - 1 for x > -1 and 3x + 1 < x - 1 for x < -1, it follows that y < x - 1 for x > -1 and y < 3x + 1 for x < -1. Of the given choices, only (2, -1) satisfies these conditions because -1 < 2 - 1 = 1.
Alternate approach: Substituting (2, -1) into the first inequality gives -1 < 3(2) + 1, or -1 < 7, which is a true statement. Substituting (2, -1) into the second inequality gives 2 - (-1) > 1, or 3 > 1, which is a true statement. Therefore, since (2, -1) satisfies both inequalities, it is a solution to the system.
Choice A is incorrect because substituting -2 for x and -1 for y in the first inequality gives -1 < 3(-2) + 1, or -1 < -5, which is false. Choice B is incorrect because substituting -1 for x and 3 for y in the first inequality gives 3 < 3(-1) + 1, or 3 < -2, which is false. Choice C is incorrect because substituting 1 for x and 5 for y in the first inequality gives 5 < 3(1) + 1, or 5 < 4, which is false.
y < 3x +1
y < x-1
Since 3x + 1 > x - 1 for x > -1 and 3x + 1 < x - 1 for x < -1, it follows that y < x - 1 for x > -1 and y < 3x + 1 for x < -1. Of the given choices, only (2, -1) satisfies these conditions because -1 < 2 - 1 = 1.
Alternate approach: Substituting (2, -1) into the first inequality gives -1 < 3(2) + 1, or -1 < 7, which is a true statement. Substituting (2, -1) into the second inequality gives 2 - (-1) > 1, or 3 > 1, which is a true statement. Therefore, since (2, -1) satisfies both inequalities, it is a solution to the system.
Choice A is incorrect because substituting -2 for x and -1 for y in the first inequality gives -1 < 3(-2) + 1, or -1 < -5, which is false. Choice B is incorrect because substituting -1 for x and 3 for y in the first inequality gives 3 < 3(-1) + 1, or 3 < -2, which is false. Choice C is incorrect because substituting 1 for x and 5 for y in the first inequality gives 5 < 3(1) + 1, or 5 < 4, which is false.
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y < 3x +1x - y >1Which of the following ordered pairs (x, y) satisfies the system of inequalities above?a)(−2, −1)b)(−1, 3)c)(1, 5)d)(2, −1)Correct answer is option 'D'. Can you explain this answer?
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