Show that the x-coordinates satisfy the equation

The line L has the equation y+2x=12 and the curve C has equation y=x^2-4x+9.
(i) show that the x-coooridinates of the points of intersection of L and C satisfy the equation x^2-2x-3=0
(ii) hence find the coordinates of the points of intersection of L and C.
Thank you :)

y=x^2-4x+9
y= -2x+12 Subtract the second from the first to eliminate y.

0 = x^2 - 2x - 3
0 = (x-3)(x+1) Set each factor = 0 and solve for x.
x=3 or x=1 Now, substitute for x to find y.
y = -2(3)+12
y=6

y=-2(1)+12
y=10

So, the solutions are (3,6) or (1,10)

This is not right. If x+1=0, then x=-1.

(1,10) is not on the parabola:(

Report Abuse

The line and parabola will intersect when
y=-2x+12= x^2-4x+9

Add (2x-12) to both sides:

0= x^2-2x-3

II) factor : 0= (x-3)(x+1)

X=3 or -1

Plug back into the line:

Y= -2(3)+12=6
y=-2(-1)+12=14

The points are (3,6) and (-1,14)

Hoping this helps!