Second one:
x=y
y =x^2+3x-3
Substitute x = y into the second equation
y = y^2 +3y-3
0 = y^2 +2y -3 factor
0 = (y+3)(y-1) so y = -3 or 1 and since x= y
-3,-3 or 1,1 are solutions
Note, RP
P = (12, -4)
P' = ( 18, - 6)
We added 6 to the x coordnate of P to get the x coordinate of P'
And we subtracted 2 from the y coordinate of P to get the y coordinate of P'
So...we need to do the same to the coordinates of Q...so we have
(-16 + 6, 8 - 2) = (-10, 6) = Q'
x = y (1)
y = x^2 + 3x -3 (2)
Sub (1) into (2)
x = x^2 +3 x - 3 subtract x from both sides
0 = x^2 + 2x - 3 factor
0 = ( x + 3) ( x - 1)
Setting both of the factors equal to 0 we have that
x + 3 = 0 x - 1 = 0
x = - 3 x = 1
Note..if x = y .....then (1, 1) is a solution ⇒ "C"