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# Does the line with equation ax+by=c cross the x-axis?

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Does the line with equation ax+by=c cross the x-axis? [#permalink]

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04 May 2016, 09:18
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Hi guys!

I took recently Exam 5 (from Gmat Prep Exam Pack 2) and I'm struggling with the following question:

Does the line with equation ax+by=c, where a,b and c are real constants, cross the x-axis?
(1) b ≠ 0
(2) ab>0

Here is my solution: I solved the equation for y, so that I got y=-ax/b + c/b. If the line crosses the x-axis, then there should be a point on it with coordinates (0,y) or otherwise, y=c/b
Therefore, b is not allowed to be 0 ( Statement 1) and there must be y, such that it is c/b (i don't have this information). Hence, my solution is E.
However, this is not the official answer ...
[Reveal] Spoiler: OA

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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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04 May 2016, 09:36
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if b is not equal to zero then if a equal to zero then it will definitely not pass by x axis where as when a is non zero may pass so 1st statement is not sufficient.
if ab>0 the either both are positive or both are negative also non of them as zero. Hench there will always be ax+by hence always a slope(-a/b) and if a line always has slope it will always pass through x axis. So the answer can be given only by statement 2 hence B is the answer.
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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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05 May 2016, 11:09
aishkar wrote:
if b is not equal to zero then if a equal to zero then it will definitely not pass by x axis where as when a is non zero may pass so 1st statement is not sufficient.
if ab>0 the either both are positive or both are negative also non of them as zero. Hench there will always be ax+by hence always a slope(-a/b) and if a line always has slope it will always pass through x axis. So the answer can be given only by statement 2 hence B is the answer.

Fix me if i'm wrong:
Generally, we can say that if b=0, then the slope is infinite and will definitely cross the x axis (straight vertical line).
Also we can say that if -ax+c=0 the line will never pass through the x axis (straight horizontal line).

Am i right about that subject?
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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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08 May 2016, 20:00
by = -ax + c

y = -(a/b)*x + c/b

if x = 0, then y = c/b

and if y = 0, then

(a/b)*x = c/b

x = c/a........., we need a!= 0

this is valid only in B) Hence B is the ans.....can someone confirm this?
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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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06 Jun 2016, 10:25
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aniketm.87@gmail.com wrote:
by = -ax + c

y = -(a/b)*x + c/b

if x = 0, then y = c/b

and if y = 0, then

(a/b)*x = c/b

x = c/a........., we need a!= 0

this is valid only in B) Hence B is the ans.....can someone confirm this?

I am wasn't sure what you meant in the last line with a!=0

My thinking for the last line following your method:

We know that x = $$\frac{c}{a}$$

The question is asking us: Is there a value x for when y equals 0? The only circumstance when x = $$\frac{c}{a}$$ will not have an actual value is if a = 0,then the answer is undefined and there is not value of x for when y = 0.

Thus, Stem 2 tells us that a*b > 0, which means they are both positive or negative and thus, there will always be a value of x when y = 0.

Hope it helps!
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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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07 Jun 2016, 00:03
B

to NOT cross x axis constant a=0

1)nothing about a is given . a=0 or a is not eq to 0

2)ab>0 a,b =+ve or a,b+-ve but surely not 0. that means line can have either +ve or -ve slope.
Suff

hope it helps

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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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07 Oct 2016, 07:34
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dgeorgie wrote:
Hi guys!

I took recently Exam 5 (from Gmat Prep Exam Pack 2) and I'm struggling with the following question:

Does the line with equation ax+by=c, where a,b and c are real constants, cross the x-axis?
(1) b ≠ 0
(2) ab>0

Here is my solution: I solved the equation for y, so that I got y=-ax/b + c/b. If the line crosses the x-axis, then there should be a point on it with coordinates (0,y) or otherwise, y=c/b
Therefore, b is not allowed to be 0 ( Statement 1) and there must be y, such that it is c/b (i don't have this information). Hence, my solution is E.
However, this is not the official answer ...

the question asks whether the line is parallel to x axis or not

slope = -a/b if = 0 then line is parallel if not then it definitely crosses the x axis

from1 ...no idea about a .... insuff

from 2

neither a nor b is 0 and they have the same sign thus slope is -ve and ll defo cross the x axis

B

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Re: Does the line with equation ax+by=c cross the x-axis? [#permalink]

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14 Oct 2017, 04:20
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Re: Does the line with equation ax+by=c cross the x-axis?   [#permalink] 14 Oct 2017, 04:20
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