AM-1440

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

.

$y = \dfrac{10+\sqrt{10}}{3}$ or $y = \dfrac{10-\sqrt{10}}{3}$
$y = -3$ or $y = \dfrac{10}{3}$
$y = 3$ or $y = -\dfrac{10}{3}$
$y = -3$ or $y = -\dfrac{10}{3}$

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