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For what values of k will the pair of equations 3x + 4y = 12 and kx +
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13 Apr 2007, 00:22
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For what values of k will the pair of equations 3x + 4y = 12 and kx + 12y = 30 does not have a unique solution? A. 12 B. 9 C. 3 D. 7.5 E. 2.5
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Joined: 14 Jan 2007
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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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13 Apr 2007, 02:51
A system of linear equations with a unique solution is characterized by the graphs of two lines whose intersection is a single point, and the coordinates of this point satisfy both equations.
So we have to find out the the value K so that the lines become parallel. Parallel lines don't intersect each other. That's why having no unique solution.
Two parallel lines have their slopes equal.
Slope of the line 3x+4y = 12, = 3/4
Putting K =9 in the line kx+12y = 30 , slope of this line = 3/4
Hence for k =9 the second line is parallel to the first one. Hence the lines will not have a unique solution.




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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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16 May 2016, 01:24
To solve two variables we need two distinct equations.
If X and Y are in the same ratio in both equations we cannot solve it.
Y1:Y2 4:12 1:3
So if X1:X2 is in the ratio 1:3 there is no distinct equation 1:3 3:9
(B) If X = 9 there is no solution.



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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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13 Apr 2007, 03:00
(B) as well... I agree with what vshaunak@gmail.com said above
For 2 equations of line, we have 3 possible cases:
> 1 point intersect the 2 lines = 2 different slopes for the lines
> No intersection = Same slopes and different Yinterceptors
> Infinite number of interesections = Same slopes and same Yinterceptors
So, the question just asks us for which value of k, the slopes are equal.
o 3x+4y = 12
<=> y = 3/4 * x + 12
o kx+12y = 30
<=> y = k/12 * x + 30/12
By equalizing the 2 slopes, we have:
k/12 = 3/4
<=> k = 12*3/4 = 9



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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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09 Jan 2012, 00:47
Hi Guys, let me know if this approach is correct(its a shortcut though):) solving the two eq simultaneously, we get kx9x=18 so for any value except 9 for K we ill have a unique solution. so 9 is our answer.



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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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13 Apr 2007, 06:08
2x+4y = 12 > 4y = 122x > y = 0.5x+3
kx+12y = 30 > 12y = kx+30 > y = kx/12 +2.5
The pairs will not have a unique solution if the lines are parallel. To find this, just make sure both lines have similar slopes. Above, I have place the equations in the standard straightline equation y = mx+c where m is the gradient of the line and c is the yintercept.
so since y = 0.5x+3 has a gradient of 0.5, then we must make sure y = kx/12+2.5 has a gradient of 0.5 too. To have this, we need k = 9.



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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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18 Jan 2016, 07:45
A linear equation in two variables may have : 1 solution(intersecting lines), infinite solution(overlapping lines) or no solution (parallel lines) For a system of equations to not have a unique solution, there should either be no solution or infinite solutions. ax+by= c px+qy=r These will have no solution when : (a/p) = (b/q) =/= (c/r) These will have infinite solutions when : (a/p) = (b/q) = (c/r) As 4/12 =/= 12/30, thus the system should not have any solution. 4/12 = 1/3 thus 3/k = 1/3 k = 3*3 = 9.
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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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15 May 2016, 22:45
i approached this problem in slightly different way,
we have 2 equations 1. 3x + 4y = 12  > 9x + 12y = 36
2. kx + 12y = 30
substract 12, we get (9K)x = 6
i.e. x = 6/(9k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B



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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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19 Oct 2016, 05:59
This can also be approached this way.
Multiply 3x+4y=12 with 3 and replace 12 y with 30kx.
This gives us x(9k)6. Hence, x= 6/(9k). We get value for x for everything besides k=9 as that makes the denominator 0.
Hope this helps



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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +
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