Question

A curve with equation y = x^2 + 2x + 3 crosses a straight line with equation y = x+9 in two places. Find the coordinates of the two points where the lines intersect.
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Answer 1

Got you fam or whatever people say....


We have equation 1 and 2
1. $y= x^{2} +2x+3$
2. $y=x+9$

Because equation 2 is simple and isn't quadtratic, we will insert 2 into 1,

$x+9= x^{2} +2x+3$ 
$0= x^{2} +x-6$ 

Then factor
x² +x -6=0
(x+3)(x-2)=0
x= -3, 2

Then using the values of x insert into either equation 1 or 2 to find y. I'm doing 2 because I'm lazy

y= x+9

when x=-3
y=x+9
  = -3+9
  = 6

(-3,6)

when x =2
y=x+9
  = 2+9
  = 11

(2,11)

Hence the co-ordinates are (2,11) and (-3,6)