Question

Find the value of k if kx+y=10 and ky-x=7 has unique solution.

Answer 1

kx+y=10
ky-x=7 in standard form -x+ky=7

condition for unique soln.
a1/a2≠b1/b2
∵k/-1≠1/k
   k*k≠-1*1
   k²≠-1
   k=+-1
            

Answer 2

The given two equations will have a unique solution for all real values of k.

Step-by-step explanation:

The given equations are kx + y = 10 .......... (1) and

ky - x = 7 .......... (2)

Now, arranging in slope-intercept form from the equation (1) we get

y = - kx + 10  ......... (3) and

$y = \frac{1}{k} x + \frac{7}{k}$ ........... (4)

Hence, the product of the slope of equations (3) and (4) will be $(- k \times \frac{1}{k}) = - 1$.

Therefore, the given two equations are perpendicular to each other.

So, the equations (1) and (2) will have a unique solution for all real values of k. (Answer)