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In the xy-plane, does the line y = 2x - 1 contain the point (p,q)?
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Hoozan
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In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? [#permalink] New post  14 Feb 2021, 04:28
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In the xy-plane, does the line y = 2x - 1 contain the point (p,q)?

(1) (2p - 1 - q)(3p + 7 - q) = 0
(2) (5p + 2 - q)(1 - 2p + q) = 0
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globaldesi
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Re: In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? [#permalink] New post  14 Feb 2021, 18:14
FS 1:

2p-1= q
3p+7=q

Not sufficient

FS 2:

2p-1 = q or
5p+2=q

combine
these three equation either can be equal to zero , hence NS
E
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sthahvi
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Re: In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? [#permalink] New post  17 Feb 2021, 10:03
globaldesi wrote:
FS 1:

2p-1= q
3p+7=q

Not sufficient

FS 2:

2p-1 = q or
5p+2=q

combine
these three equation either can be equal to zero , hence NS
E


thank you for your explanation,
but can I ask why it can't be B coz 5p+2 could be 0 ?
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Hoozan
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In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? [#permalink] New post  17 Feb 2021, 10:25
sthahvi wrote:
globaldesi wrote:
FS 1:

2p-1= q
3p+7=q

Not sufficient

FS 2:

2p-1 = q or
5p+2=q

combine
these three equation either can be equal to zero , hence NS
E


thank you for your explanation,
but can I ask why it can't be B coz 5p+2 could be 0 ?


Hi sthahvi,

We are given (5p + 2 - q)(1 - 2p + q) = 0. This means that either (5p + 2 - q) = 0 OR (1 - 2p + q) = 0 OR both are = 0.

If (5p + 2 - q) = 0 then upon simplification we get q = 5p + 2 as what globaldesi correctly explained. So yes, you a right that B cannot be our answer since we get two values of q.

That's precisely why E is our answer. Since even after combining the two statements we get 3 values of q (despite having one value common in both the statements we cannot conclude that to be our answer)
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sthahvi
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Re: In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? [#permalink] New post  17 Feb 2021, 10:28
Hoozan wrote:
sthahvi wrote:
globaldesi wrote:
FS 1:

2p-1= q
3p+7=q

Not sufficient

FS 2:

2p-1 = q or
5p+2=q

combine
these three equation either can be equal to zero , hence NS
E


thank you for your explanation,
but can I ask why it can't be B coz 5p+2 could be 0 ?


Hi sthahvi,

We are given (5p + 2 - q)(1 - 2p + q) = 0. This means that either (5p + 2 - q) = 0 OR (1 - 2p + q) = 0 OR both are = 0.

If (5p + 2 - q) = 0 then upon simplification we get q = 5p + 2 as what globaldesi correctly explained. So yes, you a right that B cannot be our answer since we get two values of q.

That's precisely why E is our answer. Since even after combining the two statements we get 3 values of q (despite having one value common in both the statements we cannot conclude that to be our answer)


thank you
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