Question

5m+1n=2 ; 6m-3n=1 Solve the simultaneous equation
​

Answer 1

5m+1n=2.......(1)

6m-3n=1........(2)

(1)×6=> 30m+6n=12.....(3)

(2)×5=>. 30m-15n=5......(4)

subtraction of (4) from(3)

30m+6n-(30m-15n)=12-15

21n=-3

n=-1/7

5m+n=2

5m-1/7=2

5m=2+1/7=15/7

m=(15/7)/5

m=3/7

m=3/7

n=-1/7

Answer 2

$\huge\sf\underline{♡Solution♡}$

$5m + 1n = 2......(i)$
$6m - 3n = 1......(ii)$

Solving by the method of comparison,

From equation (i),

$5m = 2 - 1n$
$m = \frac{2 - 1n}{5} .......(iii)$

From equation (ii),

$6m = 1 + 3n$
$m = \frac{1 + 3n}{6} ......(iv)$

By comparing eqn. (iii) and (iv),

$= > 5(1 + 3n) = 6(2 - 1n)$
$= > 5 + 15n = 12 - 6n$
$= > 15n + 6n = 12 - 5$
$= > 21n = 7$
$= > n = \frac{7}{21}$
$or \: n = \frac{1}{3}$

Putting the value of n in eqn. (iv),

$m = \frac{1 + 3n}{6} ......(iv)$

$= > m = \frac{1 + 3 \times \frac{1}{3} }{6}$

$= > m = \frac{1 + 1}{6}$
$= > m = \frac{2}{6}$

$or \: m = \frac{1}{3}$

Therefore, the value of m= 1/3 and n= 1/3 satisfies the equation.