Question

$\frac{x}{3} - \frac{y}{6} = \frac{5}{6}$

3x - 2y = 9
Solve Simultaneous Equation

Answer 1

Answer

x = 1 and y = -3

Explanation

Given,

$\frac{x}{3}$ - $\frac{y} {6}$ = $\frac{5} {6}$

=> $\frac{x}{3}$*$\frac{2}{2}$ - $\frac{y} {6}$ = $\frac{5} {6}$

=> $\frac{2x}{6}$ - $\frac{y} {6}$ = $\frac{5} {6}$

=>    2x-y = 5   -------------- (1)

and 3x-2y = 9 --------------- (2)

(1)*2 - (2) =>

4x - 2y - (3x - 2y) = 10-9

=> 4x-3x -2y + 2y = 1

=> x = 1

substitute x=1 in (2)

3(1) - 2y = 9

3-2y = 9

2y = 3-9

2y = -6

y = -6/2

y = -3

Answer 2

$\frac{x}{3} - \frac{y}{6} = \frac{5}{6} \\ \\ = > \frac{2x - y}{6} = \frac{5}{6} \\ \\ = > 2x - y = 5...(1)$

$3x - 2y = 9...(2)$

On solving by elimination method :

$2x - y = 5...(1) \times 3$

$3x - 2y = 9...(2) \times 2$

$6x - 3y = 15...(3)$

$6x - 4y = 18...(4)$

____________________________

On subtracting :

$y = - 3$

On putting the value of y in equation (1) :

$2x - ( - 3) = 5 \\ \\ = > 2x + 3 = 5 \\ \\ = > 2x =5 - 3 \\ \\ = > 2x = 2 \\ \\ = > x = 1$

So, the values of x and y are 1 and -3 respectively.