Find the value of $a$ for which the equation $2 x + a y = 5$ has $(1, - 1)$ as a solution, find two more solution for the equation obtained.

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Solution

$2 x + a y = 5$ has $(1, - 1)$ as its solution
$∴ 2 \times 1 + a (- 1) = 5 \Rightarrow 2 - a = 5 \Rightarrow a = - 3 ∴ 2 x - 3 y = 5$
other solutions are $(10, 5)$ and $(25, 15)$
$∵ 2 \times 10 - 3 \times 5 = 20 - 15 = 5$
and $∵ 2 \times 25 - 3 \times 15 = 50 - 45 = 5$

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Find the value of $k,$ if $x = 2, y = 1$ is a solution of the equation $2 x + 3 y = k$ . Find two more solutions of the resultant equation.

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