For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines?

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Abhishek Singh

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Coincident line should have same slope. So we get the equation 3/(-1) = 6/(-k). solving above equation we get k = 2;
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In order for two or more straight lines to be coincident, all the coefficients in a straight line must be a multiple of the corresponding coefficients in the other straight line. We have 6x-ky=-16 and this can be written as 6x-ky+16=0 Now 6x-ky+16=0 == A(3x-y+8=0) Equating the coefficients on both...
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In order for two or more straight lines to be coincident, all the coefficients in a straight line must be a multiple of the corresponding coefficients in the other straight line. We have 6x-ky=-16 and this can be written as 6x-ky+16=0 Now 6x-ky+16=0 == A(3x-y+8=0) Equating the coefficients on both sides,we get==> 6=3A or 16=8A and -k=-A ==> A=2 and k=2 read less
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Maths Tutor

a1=3 , b1=-1, c1=8 and a2=6 , b2=-k , c2=16 a1/a2= 3/6=1/2 b1/b2=-1/-k= 1/k c1/c2 = 8/16 =1/2 if a1/a2=b1/b2=c1/c2 then two lines will be coincident 1/2=1/k=1/2 => 1/k=1/2 => k=2
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Math Magician

3/6 = (-1)/(-K) = (-8)/(-16)...So k = 2 in this case.
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An Experienced Trainer

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if lines are coincident then a1/a2=b1/b2=c1/c2 3/6=-1/-k=8/16 i.e 1/2...therefore k=2
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Mechanical engineer

Coincident lines have the same slope and the same y-intercept. So, k=2
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Maths Teacher

The value of k should be equal to 2, and thus the equations, 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines
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