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

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
Lines a and b intersect at the point where y = 0. If the equations of  [#permalink]

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07 Sep 2018, 00:02
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:38) correct 25% (02:30) wrong based on 49 sessions

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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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07 Sep 2018, 02:25
2
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 $$m= \frac{-10}{9}$$

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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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09 Sep 2018, 00:33
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, $$x=\frac{-5}{m}$$
$$\frac{-5}{m}=\frac{9}{2}$$
$$m=\frac{-10}{9}$$
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Re: Lines a and b intersect at the point where y = 0. If the equations of   [#permalink] 09 Sep 2018, 00:33
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