QJEEM18Mad248: JEE Main 2018 Mathematics - Class 12 JEEM18Mad248 Solution: The number of values of k for which the system of linear…

System of linear equation have no solution,

$$\therefore$$ determinant of coefficient = 0

$$\left|\begin{array}{cc}k+2& 10\\ k& k+3\end{array}\right|=0$$

$$\Rightarrow$$ $$$$ (k + 2) (k + 3) $$-$$ 10 K = 0

$$\Rightarrow$$ $$$$ k² $$-$$ 5k + 6 = 0

$$\therefore$$ k = 2, 3

When, k = 2 then equations become,

4x + 10y = 2

and 2x + 5y = 1

It has in finite number of solutions.

When k = 3, equations becomes

5x + 10y = 3

3x + 6y = 2

Those equation has no solutions.

$$\therefore$$ When k = 3, then system of equations have no solutions.