Solve the following systems of simultaneous linear equations by the elimination method

9 - (x - 4) = y + 7

2(x + y) = 4 - 3y

Given,

9 - (x - 4) = y + 7

⇒ 9 - x + 4 = y + 7

⇒ x + y = 13 - 7

⇒ x + y = 6 …….(i)

2(x + y) = 4 - 3y

⇒ 2x + 2y = 4 - 3y

⇒ 2x + 5y = 4 ………(ii)

Multiplying eq. (i) by 2 we get,

⇒ 2x + 2y = 12 ……..(iii)

Subtracting eq. (iii) from (ii) we get,

⇒ 2x + 5y - (2x + 2y) = 4 - 12

⇒ 5y - 2y = -8

⇒ 3y = -8

⇒ y = $-\dfrac{8}{3}$.

Substituting value of y in eq. (i) we get,

$\Rightarrow x + \Big(-\dfrac{8}{3}\Big) = 6 \\[1em] \Rightarrow x = 6 + \dfrac{8}{3} \\[1em] \Rightarrow x = \dfrac{26}{3}.$

Hence, $x = \dfrac{26}{3} \text{ and } y = -\dfrac{8}{3}$.