What is the solution of the pair of linear equations: $2 x - 3 y = 2, x + 2 y = 8$ ?

x = 2 a n d y = 4

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x = 4 a n d y = 2

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x = 4 a n d y = 4

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x = 2 a n d y = 2

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Solution

The correct option is B $x = 4 a n d y = 2$
Given,
$2 x - 3 y = 2 . . . (1)$
$x + 2 y = 8 . . . (2)$

From (2), we have,
$x = 8 - 2 y$

Substituting this value of $x$ in (1), we have,
$2 (8 - 2 y) - 3 y = 2$
i.e., $16 - 4 y - 3 y = 2 ⟹ 7 y = 14$
$⟹ y = 2$

Now, $x = 8 - 2 y ⟹ x = 8 - 2 (2) = 4$
Thus, $x = 4 a n d y = 2$

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