# Intersection of curves

• Jul 4th 2006, 10:44 AM
bobby77
Intersection of curves
The line y=2x- 3 intersects the curve y=x^2+x-15 at the points

(a)(3,3)and(4,5)
(b)(-3,-9)and(4,5)
(c)(3,3)and(-4,-11)
(d)(-3,-9)and(-4,-11).
• Jul 4th 2006, 11:21 AM
CaptainBlack
Quote:

Originally Posted by bobby77
The line y=2x- 3 intersects the curve y=x^2+x-15 at the points

(a)(3,3)and(4,5)
(b)(-3,-9)and(4,5)
(c)(3,3)and(-4,-11)
(d)(-3,-9)and(-4,-11).

At a point of intersection:

$
2x-3=x^2+x-15
$
,

so:

$
x^2-x-12=0
$

Now trying the candidates for $x$, we find that , $x=-3$ satisfies
this equation as does $x=4$, so (b) must be the answer (assuming the
$y$'s are OK which I suppose we can).

RonL