AM-1062

Linear–quadratic simultaneous equations

A Math · Secondary 4 · Hard · Linear–quadratic simultaneous equations

Solve the simultaneous equations

x+3y-5=0

x^2+y^2=13.

What is the value of

x

?

$x=\dfrac{5-3\sqrt{105}}{10}$ or $x=\dfrac{5+3\sqrt{105}}{10}$
$x=4$ or $x=\dfrac{19}{5}$
$x=-4$ or $x=-\dfrac{19}{5}$
$x=4$ or $x=-\dfrac{19}{5}$

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