Find the solution of the pair of equations and find λ if y = λx + 5

Given pair of equations is

…(i)

and …(ii)

Now, multiplying both sides of Eq. (i) by LCM (10, 5) = 10, we get

…(iii)

Again, multiplying both sides of Eq. (iv) by LCM (8, 6) = 24, we get

…(iv)

On, multiplying Eq. (iii) by 2 and then subtracting from Eq., (iv), we get

Put the value of x in Eq. (iii), we get

Given that the linear relation between x, y and is

Now, put the values of x and y in above relation, we get

Hence, the solution of the pair of equations is x = 340, y = - 165 and the required value of is