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At which point do the lines y1 = 5x - 3 and y2 = -4x + 6

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At which point do the lines y1 = 5x - 3 and y2 = -4x + 6 [#permalink] New post 31 Oct 2009, 22:36
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (01:39) correct 10% (00:52) wrong based on 114 sessions
At which point do the lines y1 = 5x - 3 and y2 = -4x + 6 intersect?

A. (1/3, 14/3)
B. (1/3, 22/3)
C. (1, -2)
D. (1, 2)
E. (3, -6)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Nov 2012, 01:48, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Lines Intersection [#permalink] New post 31 Oct 2009, 23:38
Expert's post
gmattokyo wrote:
Please see the image for the Q and options...


I think there must be a typo in line 2 definition. Line should be represented as equation. y2-4x+6 shoul be equal to something, in the way it's represented it doesn't make any sense for me. Let's find out which kind of typo there is:

y2-4x+6?

1. y1=5x-3, y2=4x+6 (meaning that - sign should be =):
5x-3=4x+6 --> x=9, y=42 --> intersect at point (9,42), no such answer choice.

2. y1=5x-3, y2-4x+6=0 (meaning that LHS equals to 0):
5x-3=4x-6 --> x=-3, y=-18 --> intersect at point (-3,-18), no such answer choice.

3. y1=5x-3, y2=-4x+6 (meaning that = sign is just missing)
5x-3=-4x+6 --> x=1, y=2 --> intersect at point (1,2), answer choice D.

So, I suppose the third option detects the typo. But it would be easier if we knew the OA to say with certainty.
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Re: Lines Intersection [#permalink] New post 31 Oct 2009, 23:45
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Re: Lines Intersection [#permalink] New post 31 Oct 2009, 23:50
Bunuel wrote:
gmattokyo wrote:
Please see the image for the Q and options...


I think there must be a typo in line 2 definition. Line should be represented as equation. y2-4x+6 shoul be equal to something, in the way it's represented it doesn't make any sense for me. Let's find out which kind of typo there is:

y2-4x+6?

1. y1=5x-3, y2=4x+6 (meaning that - sign should be =):
5x-3=4x+6 --> x=9, y=42 --> intersect at point (9,42), no such answer choice.

2. y1=5x-3, y2-4x+6=0 (meaning that LHS equals to 0):
5x-3=4x-6 --> x=-3, y=-18 --> intersect at point (-3,-18), no such answer choice.

3. y1=5x-3, y2=-4x+6 (meaning that = sign is just missing)
5x-3=-4x+6 --> x=1, y=2 --> intersect at point (1,2), answer choice D.

So, I suppose the third option detects the typo. But it would be easier if we knew the OA to say with certainty.



yes, there was a typo in the first image :) equal sign was missing... thnx for pointing that out. You got this nailed.
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Re: Lines Intersection [#permalink] New post 06 Nov 2012, 19:50
Since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other.
This gives an equation that we can solve for x
We substitute that x value in one of the line equations (it doesn't matter which) and solve it for y.

y1 = 5x - 3
y2 = -4x+6

At intersection point, y1 = y2
5x - 3 = -4x + 6
x = 1

By substituting value of x in any of the above 2 equations we get
y = 5*1 - 3
y = 2

therefore D is the answer (1,2)

Cheers,
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Re: At which point do the lines y1 = 5x - 3 and y2 = -4x + 6 [#permalink] New post 13 Oct 2013, 02:37
solving the two equations


y1 = 5x - 3
y2 = -4x+6

-____+__-__
0 =9x-9
9x =9
x=1
Now take any one of the above equations and substitute x=1 in it
we get y=2
so answer is (1,2)
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Re: At which point do the lines y1 = 5x - 3 and y2 = -4x + 6 [#permalink] New post 23 Nov 2013, 10:35
to find intersect, y would be the same for both functions

so solve

5x - 3 = -4x +6 ---> 9x = 9 ---> x = 1

fill in 1 in ether of the two given function to return y = 2

intersect is at (1,2)

answer D is correct
Re: At which point do the lines y1 = 5x - 3 and y2 = -4x + 6   [#permalink] 23 Nov 2013, 10:35
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At which point do the lines y1 = 5x - 3 and y2 = -4x + 6

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