Question

for what value of k the following pair of linear equations has infinite number of solutions x+(2k-1)y=4;kx+6y=k+6

Answer 1

Given: Two equations, x + (2k-1)y = 4,   kx + 6y = k + 6

To find:  Value of k for which the following pair of linear equations has infinite number of solutions.

Solution:

• As we have given the two equations, we first need to write the coefficients in an order.

• So the coefficients should be written as if equation is Ax + By = C,

• So, in first equation:

                 x + (2k-1)y = 4,

                A1 = 1,   B1 = (2k-1),   C1 = 4

• in second equation:

                kx + 6y = k + 6,

                A2 = k,   B2 = 6,   C2 = k+6

• Now for infinitely many solutions, we have the condition that:

                A1/A2 = B1/B2 = C1/C2

• So applying this in the above equations, we get:

                1 / k = 2k-1/6 = 4/k+6

• Now solving any two of the above, we get:

                1/k = 4/k+6

                k+6 = 4k

                3k = 6

                k = 2

Answer:

              So, for k=2, the following pair of linear equations has infinite number of solutions.

Answer 2

Step-by-step explanation:

this for the question x +(2k-1)y=4 , kx+6y=k+5