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.
Answers
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..
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.