Question

if the equation 2x-y+3=0,7x-2y+2=0and kx-y-1=0are consistent find 5he value of k and find their common solutions for that value of k​

Answer 1

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Answer 2

Step-by-step explanation:

To find the value of k and the common solution, we can use a system of equations:

2x - y + 3 = 0 ...(1)

7x - 2y + 2 = 0 ...(2)

kx - y - 1 = 0 ...(3)

We can solve this system of equations by first using equations (1) and (2) to eliminate y:

2x - y + 3 = 0 ...(1)

7x - 2y + 2 = 0 ...(2)

4x + 6 = 0

4x = -6

x = -3/2

Now we can substitute x = -3/2 into equation (1) or (2) to solve for y:

2(-3/2) - y + 3 = 0

-3 - y + 3 = 0

y = -0

Therefore, the solution to the system of equations is (x, y) = (-3/2, 0).

To check the consistency of the third equation, we can substitute the values of x and y into equation (3):

k(-3/2) - 0 - 1 = 0

-3k/2 - 1 = 0

k = -2/3

So, the value of k for which the system of equations is consistent is k = -2/3.

Therefore, the common solution to the system of equations is (x, y) = (-3/2, 0) when k = -2/3.