Solve for x and y: 0.3x + 0.5y = 0.5, 0.5x + 0.7y = 0.74

1.	Solve for x and y: 0.3x + 0.5y = 0.5, 0.5x + 0.7y = 0.74
Answer» The given system of equations is 0.3x + 0.5y = 0.5 …….(i) 0.5x + 0.7y = 0.74 …….(ii) Multiplying (i) by 5 and (ii) by 3 and subtracting (ii) from (i), we get 2.5y - 2.1y = 2.5 - 2.2 ⇒ 0.4y = 0.28 ⇒ y = \(\frac{0.28}{0.4}\) = 0.7 Now, substituting y = 0.7 in (i), we have 0.3x + 0.5 × 0.7 = 0.5 ⇒ 0.3x = 0.50 – 0.35 = 0.15 ⇒ x = \(\frac{0.15}{0.3}\) = 0.5 Hence, x = 0.5 and y = 0.7.

Answer»

The given system of equations is

0.3x + 0.5y = 0.5 …….(i)

0.5x + 0.7y = 0.74 …….(ii)

Multiplying (i) by 5 and (ii) by 3 and subtracting (ii) from (i), we get

2.5y - 2.1y = 2.5 - 2.2

⇒ 0.4y = 0.28

⇒ y = \(\frac{0.28}{0.4}\) = 0.7

Now, substituting y = 0.7 in (i), we have

0.3x + 0.5 × 0.7 = 0.5

⇒ 0.3x = 0.50 – 0.35 = 0.15

⇒ x = \(\frac{0.15}{0.3}\) = 0.5

Hence, x = 0.5 and y = 0.7.

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