Question

For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines​

Answer 1

Answer:

Step-by-step explanation:

Coincident means, the two lines lie on top of each other.

So naturally they both have the same slope.

y = mx+c has m as slope

So, 3y = 2x+10 has slope => y = 2/3*x + 10/3 -->(1)

slope = 2/3

Then for second line

ky = -3x -15, the only way we can make this line have a slope 2/3 is multiply by -2/9 on both sides

=> -2/9 k y = 2/3 x +10/3 ---> (2)

Now if we compare (1) and (2) we see that RHS is equal for both

therefore LHS will also be equal

So,

-2/9 k*y = 1*y

or k = -9/2