Question

find the value of k which the system of equations has a unique solution Kx+ 2 y =5
3x+y=1​

Answer 1

Question

Find the value of k for which the system kx+2y =5 ; 3x+y = 1 has a unique solution.

Solution

The general form for a pair of linear equations in two variables x and y is

$\sf{a _{1}x + b_{1}y + c_{1} = 0} \\ \sf{a _{2}x + b_{2}y + c_{2} = 0}$

Condition for the unique solution

$\sf{\frac{ a_{1} }{ a_{2} } ≠ \frac{ b_{1}}{ b_{2} } }$

Now the given equation are

Kx+2y= 5

3x+ y = 1

since the equation have a unique solution then

$\sf{ \implies \frac{k}{3} ≠ \frac{2}{1} }\\ \\ \sf{ \implies \: k ≠ 6}$

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