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Lines a and b intersect at the point where y = 0. If the equations of

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Lines a and b intersect at the point where y = 0. If the equations of  [#permalink]

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New post 07 Sep 2018, 01:02
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Lines a and b intersect at the point where y = 0. If the equations of lines a and b, respectively, are 5y + 4x = 18 and 5y – mx = 5, what is the value of m?


A. 15/2

B. 9/2

C. -2/3

D. -10/9

E. -3/2

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Re: Lines a and b intersect at the point where y = 0. If the equations of  [#permalink]

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New post 07 Sep 2018, 03:25
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Bunuel wrote:
Lines a and b intersect at the point where y = 0. If the equations of lines a and b, respectively, are 5y + 4x = 18 and 5y – mx = 5, what is the value of m?


A. 15/2

B. 9/2

C. -2/3

D. -10/9

E. -3/2


Since the lines intersect where y=0, this means that the lines intersect at X-axis.

to calculate the point of intersection, both the lines will share the common point, let it be (a,b).
but b=0 [already mentioned in the question.
therefore substituting (a,0) in both the equations we get:
\(0 + 4a = 18\)
\(a=\frac{9}{2}\)

and \(– ma = 5\)
using a calculated above \(m=\frac{-(5*2)}{9}\)
Hence the \(m= \frac{-10}{9}\)

Answer: D
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Re: Lines a and b intersect at the point where y = 0. If the equations of  [#permalink]

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New post 09 Sep 2018, 01:33
1
Bunuel wrote:
Lines a and b intersect at the point where y = 0. If the equations of lines a and b, respectively, are 5y + 4x = 18 and 5y – mx = 5, what is the value of m?


A. 15/2

B. 9/2

C. -2/3

D. -10/9

E. -3/2


Equations of the lines are as follows:
\(y=\frac{-4}{5}x+\frac{18}{5}\)
\(y=\frac{m}{5}x+1\)
Since, the lines intersect at y=0, the x values for both the lines must be same at that point.
From line a, \(x=\frac{9}{2}\)
From line b, \(x=\frac{-5}{m}\)
\(\frac{-5}{m}=\frac{9}{2}\)
\(m=\frac{-10}{9}\)
Answer D.
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Re: Lines a and b intersect at the point where y = 0. If the equations of &nbs [#permalink] 09 Sep 2018, 01:33
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