Solve :

0.04x + 0.02y = 5
and 0.5(x - 2) - 0.4y = 29

Given:

0.04x + 0.02y = 5 ……………….(1)
0.5(x - 2) - 0.4y = 29 ……………….(2)

Multiplying equation (1) by 100:

⇒ (0.04x + 0.02y = 5) x 100

⇒ 4x + 2y = 500 ……………….(3)

Multiplying equation (2) by 10:

(0.5(x - 2) - 0.4y = 29) x 10

⇒ 5(x - 2) - 4y = 290

⇒ 5x - 10 - 4y = 290

⇒ 5x - 4y = 290 + 10

⇒ 5x - 4y = 300 ……………….(4)

Multiplying 2 in equation (3), we get

⇒ (4x + 2y = 500) x 2

⇒ 8x + 4y = 1,000 ……………….(5)

Adding equation (4) and (5), we get:

$\begin{matrix} & 8x & + & 4y & = & 1,000 \ & 5x & - & 4y & = & 300 \ & & & & & \ \hline & 13x & & & = & 1,300 \ \Rightarrow &x & & & = & \dfrac{1300}{13} \ \end{matrix}$

⇒ x = 100

Substituting the value of x in equation (4), we get:

⇒ 5 $\times$ 100 - 4y = 300

⇒ 4y = 500 - 300

⇒ 4y = 200

⇒ y = $\dfrac{200}{4}$ = 50

Hence, x = 100 and y = 50.