Find the values of x at the point of intersection of the curve (y = x^{2} + 2x – 3) and the lines (y + x = 1).
-
A.
(1, -2) -
B.
(0, 4) -
C.
(2, -3) -
D.
(1, -4)
Correct Answer: Option D
Explanation
Equate the equation of the curve and the line in order to find their point of intersection ie The values of y in both equations.
(y + x = 1 implies y = 1 – x)
(x^{2} + 2x – 3 = 1 – x)
(x^{2} + 2x + x – 3 – 1 = 0 implies x^{2} + 3x – 4 = 0)
((x – 1)(x + 4) = 0)
(x = (1, -4))