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Two lines represented by the equations y x 1 and y x2 3 intersect at p

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Carcass
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Two lines represented by the equations y x 1 and y x2 3 intersect at p [#permalink] New post   19 Feb 2021, 03:38
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Two lines represented by the equations \(y=x+1\) and \(y=2x+3\) intersect at point P. What are the coordinates of P?

(–2, –1)
(–1, 2)
(1, –2)
(2, –1)
(1, 2)


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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A
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Re: Two lines represented by the equations y x 1 and y x2 3 intersect at p [#permalink] New post   19 Feb 2021, 05:23
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Carcass wrote:
Two lines represented by the equations \(y=x+1\) and \(y=2x+3\) intersect at point P. What are the coordinates of P?

(–2, –1)
(–1, 2)
(1, –2)
(2, –1)
(1, 2)



To find the coordinates of point \(P (x, y)\), equate \(y\) or \(x\) of both the equations;

\(x + 1 = 2x + 3\)

\(x = -2\)

So, \(P = (-2, y)\)
Only one option has a x-coordinate to -2

Hence, option A
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Two lines represented by the equations y x 1 and y x2 3 intersect at p [#permalink] New post   19 Feb 2021, 05:24
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KarunMendiratta wrote:
Carcass wrote:
Two lines represented by the equations \(y=x+1\) and \(y=2x+3\) intersect at point P. What are the coordinates of P?

(–2, –1)
(–1, 2)
(1, –2)
(2, –1)
(1, 2)



To find the coordinates of point \(P (x, y)\), equate \(y\) or \(x\) of both the equations;

\(x + 1 = 2x + 3\)

\(x = -2\)

So, \(P = (-2, y)\)
Only one option has a x-coordinate as -2

Hence, option A
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Two lines represented by the equations y x 1 and y x2 3 intersect at p [#permalink] New post   22 Apr 2021, 17:13
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Quickly sketch out on a coordinate system, it shows that clearly that the point of intersection is going to be in the negative X range, so eliminate C, D, E.

Next, can we get a positive integer for Y if we use a negative integer for X in the equation Y=X+1? No, so eliminate B.

Answer choice A is the only one left.
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Re: Two lines represented by the equations y x 1 and y x2 3 intersect at p [#permalink] New post   08 May 2023, 17:17
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Two lines represented by the equations y x 1 and y x2 3 intersect at p [#permalink]
08 May 2023, 17:17
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