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 is D

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. 

\(y + x = 1 \implies y = 1 - x\)

\(x^{2} + 2x - 3 = 1 - x\)

\(x^{2} + 2x + x - 3 - 1 = 0 \implies x^{2} + 3x - 4 = 0\)

\((x - 1)(x + 4) = 0\)

\(x = (1, -4)\)