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# Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis

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Retired Moderator
Joined: 29 Apr 2015
Posts: 868
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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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12 May 2015, 11:51
4
00:00

Difficulty:

45% (medium)

Question Stats:

60% (00:56) correct 40% (01:26) wrong based on 197 sessions

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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

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Joined: 04 Jan 2015
Posts: 1598
Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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12 May 2015, 22:21
3
Hi reto,

The question gives us two line segments and asks us the height of the intersection point of these line segments from the x- axis i.e. we need to find the y coordinate of the intersection point of the line segments.

We need to solve the equations of the line segments to find out the value of $$y$$

$$y=√3x−2$$ ..... (1)

$$y=2√3x−5$$..... (2)

Multiplying equation (1) by 2 and subtracting equation (2) from equation (1) would give us

$$y = 1$$

Hence the answer is Option C

Hope it helps!

Regards
Harsh
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Director
Joined: 23 Jan 2013
Posts: 598
Schools: Cambridge'16
Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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07 Oct 2015, 03:35
1
1
Just solve two equations for y:
y=sqrt3*x-2
y=2sqrt3*x-5

x=(y+2)/sqrt3

substitute for x

2sqrt3*(y+2/sqrt3)-5
y=2y+4-5
y=1

C
Math Expert
Joined: 02 Aug 2009
Posts: 5952
Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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17 Feb 2017, 19:49
reto wrote:
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

Hi..

Most important point..
you can easily find value of x and y as two equations and two variables..
BUT height from x axis will be value of y and not value of x..

y=√3·x−2 and y=2√3·x−5 ...
So y=√3·x−2 =2√3·x−5 .......√3·x=3......X=√3

So y =√3*x-2=√3*√3-2=3-2=1

C
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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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19 Feb 2017, 09:59
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

If same question is ask in term of x-axis should we need to eliminate "y" correct me if I am wrong
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Target#01 Q45,V20--April End

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Joined: 08 May 2011
Posts: 21
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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21 May 2017, 18:34
chetan2u wrote:
reto wrote:
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

Hi..

Most important point..
you can easily find value of x and y as two equations and two variables..
BUT height from x axis will be value of y and not value of x..

y=√3·x−2 and y=2√3·x−5 ...
So y=√3·x−2 =2√3·x−5 =>√3·x=3......X=√3

So y =√3*x-2=√3*√3-2=3-2=1

C

Hi Chetan2u ... can you breakdown the highlighted steps above?
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis   [#permalink] 21 May 2017, 18:34
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