Question

find the value of k for which the given system of equation has many solution: Kx+2y=12 , 5x-2y=4​

Answer 1

Your Question is wrong

for many solution that is infinite solutions

coefficients should be proportional

2/-2 is not equal to 12/4

that is -1 is not equal to 3

So its possible if they are parallel or intersecting

for parallel

coefficients are proportional

k/5 = 2/-2

k/5 = -1

k = -5

For unique that is intersecting

if k not equal to -5 then it would not be parallel and its not coincident also

so it would be intersecting

Answer 2

Answer:

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Mathematically the equations Written are two linear (straight lines) equations and a solution means A point where these two intersects point is ( values of x,values of y)

Since for no solution logically Both the lines should have same slopes i.e. slope Of first line should be equal To slope of the second line Therefore ;

Slope of first line = -k/2 = m1

Slope of second line = -3 = m2

Now

Put m1=m2

That means K/2 =3 now k =6

For k=6 there is no solution.

For solution any value Of k except 6 will give the solution.

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