B ) S ={(2, 2), (4,-2)}
1) Setting the system:
y + 2 = (x-4)²
And adding the 2nd Equation to the System:
y+2 = (x-4)²
2x -y - 6 =0
2) Now let's solve it by using the Addition Method:
y+2 = (x-4)²
2x -y - 6 =0 x (-1)
y+2 = (x-4)²
-2x +y + 6 =0
-------------------------
-2x +8 = (x-4)²
-2x +8 = x² -8x +16
-x²+8x -16-2x +8 =0
-x² +6x -8 =0
x² -6x +8 = 0
Factoring it we have:
(x-2)(x-4) = 0 So the solution set i
x- 2 =0
x = 2
x-4= 0
x=4
3) Plug into the first equation x = 4:
y +2 = (x-4)²
y+2 =(4-4)²
y = -2
Finally, plugging x = 2 into the same equation:
y +2 = (x-4)²
y +2 = (2 -4)²
y+2 = (-2)²
y +2 = 4
y = 4-2
y= 2
So the answer is S ={(2, 2), (4,-2)} s
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