Determine the value of $m$ and $n$ so that the pair of linear equations
$(2 m + 1) x + 3 y = 5$
$3 x + (n - 1) y = 2$
have infinite number of solutions.

Open in App

Solution

$(2 m + 1) x + 3 y - 5 = 0$
$3 x + (n - 1) y - 2$

condition for a pair of linear equations to have infinite number of solutions
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

$\frac{2 m + 1}{3} = \frac{3}{n - 1} = \frac{- 5}{- 2}$

$\frac{2 m + 1}{3} = \frac{5}{2}$

$4 m + 2 = 15$

$4 m = 13$

$m = \frac{13}{4}$

$\frac{3}{n - 1} = \frac{5}{2}$

$5 n - 5 = 6$

$5 n = 11$

$n = \frac{11}{5}$

Suggest Corrections

Similar questions

(2 m - 1) x + 3 y = 5; 3 x + (n - 1) y = 2

a

b

(2 a - 1) x + 3 y - 5 = 0

3 x + (b - 1) y - 2 = 0

(3 k + 1) x + 3 y - 5 = 0 a n d 2 x - 3 y + 5 = 0

K .

(i) For which values of a and b will the following pair of linear equations have an

infinite number of solutions?

(ii) For which value of k will the following pair of linear equations have no solution?

Join BYJU'S Learning Program