Question

2x+3y-7==0and (m-1)x+(m+1)y=(3m-1)

Answer 1

Solution:

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Given:

              The two equations have unique solution,.

2x +3y - 7 = 0 ...(i)

(m-1)x + (m+1)y = 3m - 1

=> (m-1)x + (m+1)y -3m + 1 = 0,..(ii)

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To find :

The value of m

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We know that,

The equations of the form,

$a_1x + b_1y +c_1 =0$

&

$a_2x +b_2y + c_2 = 0$

$\frac{a_1}{a_2} ≠ \frac{b_1}{b_2}$ (for infinitely many solution)

So,

=> $\frac{2}{m-1}$ ≠ $\frac{3}{m+1}$

=> $2(m+1)$ ≠ $3(m-1)$

=> 2m + 2 ≠ 3m - 3

=> 2 + 3 = 3m - 2m

=> ∴ m = 5,

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