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# In the rectangular quadrant system shown above, which quadrant, if any

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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08 Aug 2016, 08:15
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Difficulty:

45% (medium)

Question Stats:

70% (01:20) correct 30% (01:38) wrong based on 172 sessions

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In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x + 5y = −2?

A. none
B. I
C. II
D. III
E. IV

Attachment:

2016-08-08_2014.png [ 1.3 KiB | Viewed 2113 times ]

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08 Aug 2016, 08:25

Convert the equation to the form y=mx+c.

$$3x + 5y = -2$$ is $$y = -3x/5 - 2/5$$ And applying values for $$x$$ as 0,1,-1 we can see that it doesn't pass through I quadrant.
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08 Aug 2016, 09:32
Bunuel wrote:

In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x + 5y = −2?

A. none
B. I
C. II
D. III
E. IV

Attachment:
2016-08-08_2014.png

Simple way to solve this questions is to draw the line on the coordinate plan by taking the x-intercept and y-intercept. We will get a line that won't pass through 1st quadrant.

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08 Aug 2016, 09:48
3x + 5y= -2
rearranging the equation:
y=-(3/5)x-(2/5)
slope is negative
line passes through either II,I ,and IV quadrants or II,III, and IV quadrants.
Y intercept is negative => line passes through II,III and IV quadrants.
Any point (x,y) in I quadrant will not satisfy the given equation.

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08 Aug 2016, 22:19
4
Bunuel wrote:

In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x + 5y = −2?

A. none
B. I
C. II
D. III
E. IV

Attachment:
2016-08-08_2014.png

3x + 5y = -2

Put x = 0, y = -2/5
Put y = 0, x = -2/3

Plot the two points. You will see that the line will pass through II, III and IV quadrants but not through quadrant I.

Also note that a line cannot pass through all 4 quadrants...
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09 Aug 2016, 18:26
The equation is 3x + 5y = -2. Since both x and y are positive in the 1st quadrant, sum of 2 positive numbers can never yield a negative.

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24 Mar 2018, 20:25
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Re: In the rectangular quadrant system shown above, which quadrant, if any &nbs [#permalink] 24 Mar 2018, 20:25
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