Solve the pair of linear equation $: 2 X - 5 Y - 4 = 0, 4 X - 8 Y = 8.$

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Solution

Given first equation is
$2 X - 5 Y = 4 . . . (1)$

Second equation,
$4 X - 8 Y = 8$
$\Rightarrow X - 2 Y = 2$
$\Rightarrow X = 2 + 2 Y$

From equation (1)
$2 (2 + 2 Y) - 5 Y = 4$
$4 + 4 Y - 5 Y = 4$
$4 - Y = 4$
$4 - 4 = Y$
So,
$Y = 0$

Substituting the value of $Y$ in (1),
$2 X - 5 (0) = 4$
$2 X = 4$
$X = 2$

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