Question

The value of k for which the line 3x+4y=5, 5x+4y=4 and kx+4y=6 meet at a point is
(A) 1. (B) 2. (C) 3. (D) 4.​

Answer 1

Answer:

K = 1

Step-by-step explanation:

Finding point of intersection of lines

3x + 4y = 5

5x + 4y = 4

The point of intersection is

(-1/2,13/8).

The third line also passes through this point.

By substituting values in the equation

kx + 4y = 6

-k/2 + 13/2 = 6

On solving equation we get

k = 1..

Answer 2

Given: The lines 3x+4y=5, 5x+4y=4 and kx+4y=6 meet at a point.

To find: Value of k

Solution: When equations of two lines are solved, the value of x and y is the x-coordinate and y-coordinate of their intersection point.

Here, 3x+4y= 5 and 5x+4y=4 meet at a point.

For finding the intersection point,

3x+4y = 5 ---- equation (i)

5x+4y = 4 ------ equation (ii)

Subtracting equation (i) from equation (ii),

5x+4y-(3x+4y) = 4-5

=> 5x+4y-3x-4y= -1

=> 2x = -1

=> x = -1/2

Putting x= -1/2 in equation (i),

3× -1/2 +4y =5

=> -3/2 +4y = 5

=> 4y = 5 + (3/2)

=> 4y = 10+3 / 2

=> 4y= 13/2

=> y = 13/8

Therefore, (-1/2,13/8) is the intersection point of these lines. Now, since there is only one point of intersection of these lines, it means that the line kx+4y=6 also meets the other two lines at this point.

Since the intersection point of the lines lies on every three lines, therefore (-1/2,13/8) lies on the line kx+4y= 6 and should satisfy its equation.

So,

k × -1/2 + 4 × 13/8 = 6

=> -k/2 + 13/2 = 6

=> -k+13 / 2 = 6

=> -k +13 = 6×2

=> 13-k = 12

=> k = 13-12

=> k = 1

Therefore, the value of k is option (a) 1.