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Solve the pair of equation by using the substitution method: $0.2 x + 0.3 y = 1.3; 0.4 x + 0.5 y = 2.3$ .

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x = - 3

and

y = - 2

x = 2

and

y = 2

x = 3

and

y = 2

None of these

answer is C.

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Detailed Solution

Given equations are:

0.2 x + 0.3 y = 1.3

………….(1)

0.4 x + 0.5 y = 2.3

……………(2)
From equation

(i)

, we get,

0.2 x = 1.3 - 0.3 y

\Rightarrow x = \frac{13 - 3 y}{2}

…………………(3)
Substituting

x = \frac{13 - 3 y}{2}

in equation (2),

∴ 0.4 (\frac{13 - 3 y}{2}) + 0.5 y = 2.3

\Rightarrow 2.6 - 0.6 y + 0.5 y = 2.3

\Rightarrow - 0.1 y = - 0.3

\Rightarrow y = 3

Substituting

y = 3

in equation (3),

∴ x = \frac{13 - 3 \times 3}{2}

x = 2

Therefore, option (3) is correct.

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