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The lines $2 x + y = 5$ and $x + 2 y = 4$ intersect at

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$(2, 1)$

$(\frac{5}{2}, 0)$

$(1, 2)$

$(0, 2)$

answer is B.

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Detailed Solution

$2 x + y = 5 \dots \dots (1) and x + 2 y = 4 \dots \dots (2)$

From (1)

$y = 5 - 2 x$

Put $y$ in (2)

$\begin{array}{l} x + 2 (5 - 2 x) = 4 \\ x + 10 - 4 x = 4 \\ - 3 x = 4 - 10 \\ - 3 x = - 6 \\ x = 2 \\ y = 5 - 2 (2) = 5 - 4 = 1 \end{array}$

Point is $(2, 1)$

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