find the value of k for which the following system of equations has a

1.	find the value of k for which the following system of equations has a unique solutions 1 . kx +2y= 5 , 3x+y=1
Answer» Answer: The value of k is all number EXCEPT $k=6$ Step-by-step explanation: Given : Equations $kx+2y=5,3x+y=1$ To find : The value of k for which the FOLLOWING system of equation has a unique solution. Solution : When the system of equation is in FORM $ax+by+c=0, dx+ey+f=0$ then the CONDITION for a unique solutions is $\frac{a}{d}\neq\frac{b}{e}$ Comparing, a=k , b=2 , c=-5, d=3, e=1, f=-1 Substituting the values, $\frac{k}{3}\neq\frac{2}{1}$ Cross multiply, $k\times 1\neq 2\times 3$ $k\neq 6$ Therefore, The value of k is all number except $k=6$