Question

Find the value of k if pair of linear equations 2x - 3y = 8 ,2x (k-4) - ky = k + 3​

Answer 1

To find the value of k, we can solve the pair of linear equations simultaneously and equate the coefficients of corresponding variables. We simplify the second equation, rearrange the equations, create a system of equations, and solve the system to find k = 4.

Step-by-step explanation:

To find the value of k, we can solve the pair of linear equations simultaneously and equate the coefficients of corresponding variables. First, we can simplify the second equation by distributing the 2x and ky terms. Then, we can rearrange the equations so that the x and y terms are on the left side and constants on the right. Next, we can create a system of equations by equating the coefficients of corresponding variables. Finally, we can solve the system of equations to find the value of k.

Let's go through the steps:

1. Expand the second equation: 2x(k-4) - ky = k + 3 becomes 2kx - 8x - ky = k + 3
2. Rearrange the equations: 2x - 3y = 8 and 2kx - 8x - ky = k + 3 become 2x - 3y - 8 = 0 and (2k - 8)x - ky - k - 3 = 0
3. Create a system of equations: equate the coefficients of corresponding variables: 2k - 8 = 0 and -k = -k - 3
4. Solve the system of equations: solve the first equation to get k = 4

Therefore, the value of k is 4.

Learn more about Solving linear equations