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

$x - \dfrac{2}{3}y = \dfrac{8}{3}$

$\dfrac{2x}{5} - y = \dfrac{7}{5}$

Given,

$x - \dfrac{2}{3}y = \dfrac{8}{3}$ ……..(i)

$\dfrac{2x}{5} - y = \dfrac{7}{5}$ ……..(ii)

Multiplying eq. (i) by 6 and eq. (ii) by 15 we get,

6x - 4y = 16 …….(iii)

6x - 15y = 21 ……(iv)

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

⇒ 6x - 4y - (6x - 15y) = 16 - 21

⇒ 6x - 6x - 4y + 15y = -5

⇒ 11y = -5

⇒ y = $-\dfrac{5}{11}$.

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

$\Rightarrow 6x - 15 \times -\dfrac{5}{11} = 21 \\[1em] \Rightarrow 6x + \dfrac{75}{11} = 21 \\[1em] \Rightarrow 6x = 21 - \dfrac{75}{11} \\[1em] \Rightarrow 6x = \dfrac{231 - 75}{11} \\[1em] \Rightarrow 6x = \dfrac{156}{11} \\[1em] \Rightarrow x = \dfrac{156}{66} \\[1em] \Rightarrow x = \dfrac{26}{11}.$

Hence, $x = \dfrac{26}{11} \text{ and } y = -\dfrac{5}{11}.$