Question

Find the value of k if (k-1)(2k-4) is the solution of the equation 2x-7y+10=0

Answer 1

Pair of Linear equations :

i) 2x +3y=7

ii) (k+1)x+(2k-1)y=4k+1

We know that,

For infinite solutions :

a1/a2 = b1/b2 = c1/c2

From the above equations :

a1 = 2 a2 = 3 a3 = 7

b1 = k + 1 b2 = 2k - 1 b3 = 4k + 1

2/K+1 = 3/2k-1 = 7/4k+1

2/k + 1 = 3/2k - 1

4k - 2 = 3k + 3

k = 5

Therefore, the value of k is 5.

Answer 2

Answer:

given system may be written as

x − 3y − 3 = 0

3x − 9y − 2 = 0

The given system of equation is of the form

a2x + b2y − c2 = 0 a2x + b2y − c2 = 0

Where, a1 = 1, b1 = −3, c1 = −3

a2 = 3, b2 = −9, c2 = −2

We have,