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

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x = 1, y = - 2

x = 6, y = - 7

x = 5, y = 1

x = 2, y = 3

answer is D.

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Detailed Solution

Given equations are,

0.2 x + 0.3 y = 1.3; 0.4 x + 0.5 y = 2.3

.
Considering first equation,

0.2 x + 0.3 y = 1.3

…………….(1)

\Rightarrow x = \frac{1.3 - 0.3 y}{0.2}

……………..(2)
And considering second equation,

\Rightarrow 0.4 x + 0.5 y = 2.3

………………(3)
Substitute

x = \frac{1.3 - 0.3 y}{0.2}

in equation (3),

\Rightarrow 0.4 \times (\frac{1.3 - 0.3 y}{0.2}) + 0.5 y = 2.3

\Rightarrow 0.2 \times (1.3 - 0.3 y) + 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

Substitute

y = 3

in equation (2),

0.2 x + 0.3 (3) = 1.3

\Rightarrow x = \frac{1.3 - 0.9}{0.2}

\Rightarrow x = 2

Thus, the solution is x = 2 and y = 3.
Therefore, option (4) is correct.

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