Solve the following system of equations.
$l o g_{2} x + l o g_{2} y = 1,$
$x + y = 3.$

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Solution

$x + y = 3$

${log}_{2} x + {log}_{2} y = 1 ⟹ {log}_{2} x y = 1$

$⟹ x y = 2$

$(x - y)^{2} = (x + y)^{2} - 4 x y = 3^{2} - 4.2 = 1$

$⟹ x - y = 1$

And $x + y = 3$

On solving , we get-

$x = 2, y = 1$

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