Question

2x/a + y/b = 2;;x/a -y/b =4 solve by any method ​

Answer 1

$\huge{\boxed{\text{Answer :- }}}$

♦ As we are provided

$\dfrac{2x}{a} + \dfrac{y}{b} = 2$

and

$\dfrac{x}{a} - \dfrac{y}{b} = 4$

♦ By further solving above

(1) $\dfrac{2x}{a} + \dfrac{y}{b} = 2$

$\implies \dfrac{2xb}{ab} + \dfrac{ya}{ab} = 2$

$\implies \dfrac{2bx + ay}{ab} = 2$ ......(i)

(2) $\dfrac{x}{a} - {y}{b} = 4$

$\implies \dfrac{xb}{ab} - \dfrac{ya}{ab} = 4$

$\implies \dfrac{bx - ay}{ab} = 4$ .....(ii)

♦ Now by multiplying equation (ii) by 2

$\implies \dfrac{2bx - 2ay}{ab} = 8$ ......(iii)

♦ Now subtracting (iii) from (i)

$\dfrac{2bx + ay}{ab} = 2$

$-( \dfrac{2bx - 2ay}{ab}) = -(8)$

___________________________

$\dfrac{3ay}{ab} = -6$

$\implies \dfrac{ay}{ab} = \dfrac{-6}{3}$

$\implies \dfrac{ay}{ab} = -2$

$\implies \dfrac{y}{b} = -2$

♦ Now by replacing value of

$\dfrac{y}{b}$ = 2 in $\dfrac{2x}{a} + \dfrac{y}{b} = 2$

→ $\dfrac{2x}{a} - 2 = 2$

→ $\dfrac{2x}{a} = 4$

→ $\dfrac{x}{a} = 2$

♦ So values of

→ $\bold{\dfrac{x}{a} = 2}$

→ $\bold{\dfrac{y}{b} = -2}$

♦ Or

$\bold{ x = 2a }$

$\bold{y = -2b}$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Here, we have

the given equations are

⇒ 2x/a + y/b = 2 ... (i)

⇒ x/a - y/b = 4 .... (ii)

From equation (i), we get

⇒ y/b = 2 - 2x/a

⇒ y = b(2 - 2x/a)

Putting y's value in Eq (ii), we get

⇒ x/a - y/b = 4

⇒ x/a - b/b(2 - 2x/a) = 4

⇒ x/a - 2 + 2x/a = 4

⇒ 3x/a = 6

⇒ 3x = 6a

⇒ x = 2a

Putting x's value in equation (i), we get

⇒ 2x/a + y/b = 2

⇒ 4 + y/b = 2

⇒ y/b = - 2

⇒ y = - 2b

Here, x = 2a and y = - 2b

Hence, the solution of the given system of equation is x = 2a, y = - 2b.