Solve for x and y: 0.4x + 0.3y = 1.7, 0.7x – 0.2y = 0.8.

1.	Solve for x and y: 0.4x + 0.3y = 1.7, 0.7x – 0.2y = 0.8.
Answer» The given system of equations is 0.4x + 0.3y = 1.7 …….(i) 0.7x – 0.2y = 0.8 …….(ii) Multiplying (i) by 0.2 and (ii) by 0.3 and adding them, we get 0.8x + 2.1x = 3.4 + 2.4 ⇒ 2.9x = 5.8 ⇒x = \(\frac{5.8}{2.9}\) = 2 Now, substituting x = 2 in (i), we have 0.4 × 2 + 0.3y = 1.7 ⇒ 0.3y = 1.7 – 0.8 ⇒ y = \(\frac{0.9}{0.3}\) = 3 Hence, x = 2 and y = 3.

Answer»

The given system of equations is

0.4x + 0.3y = 1.7 …….(i)

0.7x – 0.2y = 0.8 …….(ii)

Multiplying (i) by 0.2 and (ii) by 0.3 and adding them, we get

0.8x + 2.1x = 3.4 + 2.4

⇒ 2.9x = 5.8

⇒x = \(\frac{5.8}{2.9}\) = 2

Now, substituting x = 2 in (i), we have

0.4 × 2 + 0.3y = 1.7

⇒ 0.3y = 1.7 – 0.8

⇒ y = \(\frac{0.9}{0.3}\) = 3

Hence, x = 2 and y = 3.

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