AM-1256

Linear–quadratic simultaneous equations

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

The curve

6x - xy = 18

intersects the line

x - 3y - 2 = 0

at points

P

and

Q

. Find the

y

-coordinates of

P

and

Q

.

$y = \dfrac{8 + \sqrt{46}}{3}$ or $y = \dfrac{8 - \sqrt{46}}{3}$
$y = -\dfrac{1}{3}$ or $y = 6$
$y = \dfrac{1}{3}$ or $y = -6$
$y = -\dfrac{1}{3}$ or $y = -6$

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