Show that each of the following systems of equations has a unique solution and solve it:

$2 x - 3 y = 17, 4 x + y = 13.$

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Solution

$2 x - 3 y = 17, 4 x + y = 13.$

$2 x - 3 y = 17$ ---------(1)
$4 x + y = 13$ -----------(2)

multiplying equation (1) by (2)

$4 x - 6 y = 34$
$4 x + y = 13$
----------------
$5 y = 21$
$y = \frac{21}{5}$

now put this in equation no. (2)

$4 x + \frac{21}{5} = 13$
$4 x = 13 - \frac{21}{5}$
$4 x = \frac{(65 - 21)}{5}$
$4 x = \frac{44}{5}$
$4 x = \frac{44}{20} = \frac{11}{5}$

$x = \frac{11}{5}$
Hence a unique solution.

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