Question

for what value of k the equation 3x+2y=5 and kx+2y=6 has a unique solution

please give right solution with explanation​

Answer 1

Answer:

The Given pair of  linear equation is :

3x +2y = -5

3x +2y +5= 0………(1)

x -ky=2

x -ky -2 = 0…………(2)

On comparing with General form of a pair of linear equations  in two variables x & y is: a1x + b1y + c1 = 0

and   a2x+b2y + c2= 0

a1= 3, b1= 2, c= 5

a2= 1 , b2= -k , c= -2

a1/a2= 3/1 ,  b1/b2= 2/-k & c1/c2= 5/-2

Given: A pair of linear equations has a Unique solution if

a1/a2 ≠ b1/b2

3/1 ≠ 2/-k

3× -k ≠ 2

k ≠ -⅔

Hence, the value of k ≠ -⅔.

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Step-by-step explanation:

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Answer 2

Given

Two equations

1. 3 x+2y= 5

2. k x+2y= 6

Solution

General form of Linear equations in given by :-

$\sf{a_{1}x + b_{1}y + c _{1}} \\ \\ \sf{a_{2}x + b_{2}y + c _{2}}$

If the given pair have unique solution then it's written as :-

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

Now , subsitute the values -

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

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