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In the rectangular coordinate system, which quadrant/s contains at l
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15 Dec 2024, 13:05
15 Dec 2024, 13:05
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In the rectangular coordinate system, which quadrant/s contains at least one point (x, y) that satisfies the inequality \(x + 3y < 1\) ?
A. I only
B. I and II only
C. III and IV only
D. I, II and IV only
E. I, II, III and IV
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Re: In the rectangular coordinate system, which quadrant/s contains at l
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26 Dec 2024, 01:12
26 Dec 2024, 01:12
Expert Reply
We need to check the quadrant which may contain the point $\((x, y)\)$ that satisfies the inequality $\(x+3 y<1\)$
We can check the given inequality for each of the four quadrants one by one.
(Note: - As we are looking for the possibility of the inequality $x\(+3 y<1\)$ to be true for different quadrants, we will try for those points in different quadrants for which the inequality holds true)
Quadrant I - If the point $\((x, y)=\left(\frac{1}{3}, \frac{1}{6}\right)\)$, it satisfies the inequality $\(x+3 y=\frac{1}{3}+\frac{1}{2}=\frac{5}{6}<1\)$
Quadrant II - If we consider the point $\((x, y)=(-4,1)\)$, it satisfies the inequality $\(x+3 y--4+3 \times 1--4+3--1<1\)$
Quadrant III - If we consider $\((x, y)=(-3,-2)\)$, it satisfies the inequality $\(x+3 y=-2+3 x-2=-2-6=-8<1\)$
Quadrant IV - If we consider $\((x, y)=(1,-2)\)$, it satisfies the inequality $\(x+3 y=1+3 x-2=1-6=-5<1\)$
Hence all four quadrants may contain the point $\((x, y)\)$, so the answer is ( $\(E\)$ ).
We can check the given inequality for each of the four quadrants one by one.
(Note: - As we are looking for the possibility of the inequality $x\(+3 y<1\)$ to be true for different quadrants, we will try for those points in different quadrants for which the inequality holds true)
Quadrant I - If the point $\((x, y)=\left(\frac{1}{3}, \frac{1}{6}\right)\)$, it satisfies the inequality $\(x+3 y=\frac{1}{3}+\frac{1}{2}=\frac{5}{6}<1\)$
Quadrant II - If we consider the point $\((x, y)=(-4,1)\)$, it satisfies the inequality $\(x+3 y--4+3 \times 1--4+3--1<1\)$
Quadrant III - If we consider $\((x, y)=(-3,-2)\)$, it satisfies the inequality $\(x+3 y=-2+3 x-2=-2-6=-8<1\)$
Quadrant IV - If we consider $\((x, y)=(1,-2)\)$, it satisfies the inequality $\(x+3 y=1+3 x-2=1-6=-5<1\)$
Hence all four quadrants may contain the point $\((x, y)\)$, so the answer is ( $\(E\)$ ).
gmatclubot
Re: In the rectangular coordinate system, which quadrant/s contains at l [#permalink]
26 Dec 2024, 01:12
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