Question

for what value of K for which system of equation x-2y=3 and 3x+ky=1 have a unique solution​

Answer 1

For all value of k, (k ≠ 6) given system of equations have unique solution.

Given:-

Linear equations in two variables:-

• x - 2y = 3
• 3x + ky = 1

To find:-

• Value of k

Solution:-

• x - 2y - 3 = 0 ---(1)
• 3x + ky - 1 = 0 ---(2)

★ The given linear equations are in form of:-

✦ $\sf a_1 x + b_1 y + c_1 = 0$

✦ $\sf a_2 x + b_2 y + c_2 = 0$

Now We get,

✦ $\sf a_1 \;$ = 1 ; $\;\sf b_1 \;$ = -2 ; $\sf c_1 \;$ = -3

✦ $\sf a_2\;$ = 3 ; $\;\sf b_2\;$ = k ; $\;\sf c_2 \;$ = -1

★ Given Equation has unique solution:-

$:\implies\sf \dfrac{ a_1 }{ a_2 }$ ≠ $\sf \dfrac{ b_1 }{ b_2 }$

$\longrightarrow\sf \dfrac{1 }{3}$ ≠ $\sf \dfrac{-2}{k}$

$\longrightarrow\sf k ≠ -6$

For all value of k, (k ≠ 6) given system of equations have unique solution.

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