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What is the value of k if the system of linear equations shown above

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Bunuel
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What is the value of k if the system of linear equations shown above [#permalink] New post   08 Jun 2020, 11:49
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-2x - ky -9 = 0
4x – 10y + 18 = 0
What is the value of constant k if the system of linear equations shown above has infinite solutions?

A. -5
B. -1
C. 1
D. 3
E. 5
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Superman249
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Re: What is the value of k if the system of linear equations shown above [#permalink] New post   08 Jun 2020, 13:20
For two linear equation a1x+b1y+c=0; a2x+b2y+c=0

A system of Linear equation have an infinite solution; when both lines graph are exactly the same.

or a1/a2=b1/b2=c1/c2

replacing values of a1,a2,b1,b2,c1,c2 from given equations

We will have -1/2=k/10=-1/2

or k=-5
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Re: What is the value of k if the system of linear equations shown above [#permalink] New post   08 Jun 2020, 13:37
Two lines has infinite many solutions when both are parallel to each other.
Such as Equation A1X+B1Y+C1=0 & A2X+B2Y+C2=0
A1/A2=B1/B2=C1/C2
Here equations are -2x - ky -9 = 0 and 4x – 10y + 18 = 0
Therefore,
-2/4=-k/-10=-9/18
-1/2 = k/10
-10/2 = K
K = -5
Answer is A

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Re: What is the value of k if the system of linear equations shown above [#permalink] New post   09 Jun 2020, 11:40
IMO A

-2x - ky -9 = 0
4x – 10y + 18 = 0

Multiply first equation with -1 & second equation by \(\frac{1}{2}\)

2x + ky + 9 = 0
2x – 5y + 9 = 0

To have infinite solutions, both equations need to be same i.e. when k = -5 both equations will be identical and will have infinite solutions
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Re: What is the value of k if the system of linear equations shown above [#permalink] New post   11 Jun 2020, 13:54
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Bunuel wrote:
-2x - ky -9 = 0
4x – 10y + 18 = 0
What is the value of constant k if the system of linear equations shown above has infinite solutions?

A. -5
B. -1
C. 1
D. 3
E. 5


Solution:

Recall that two linear equations have an infinite number of solutions if and only if one equation is an exact multiple of the other. We see that 4 is -2 times -2 and 18 is -2 times -9. Therefore, -10 has to be also -2 times -k in order to an infinite number of solutions:

-10 = -2(-k)

-10 = 2k

-5 = k

Answer: A
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Re: What is the value of k if the system of linear equations shown above [#permalink] New post   22 Mar 2023, 12:11
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Re: What is the value of k if the system of linear equations shown above [#permalink]
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