Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x – 3\) and the lines \(y + x = 1\).
- (1, -2)
- (0, 4)
- (2, -3)
-
(1, -4)
The correct answer is: 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.
\(y + x = 1 \implies y = 1 - x\)
\(x^{2} + 2x - 3 = 1 - x\)
\(x^{2} + 2x + x - 3 - 1 = 0 \implies x^{2} + 3x - 4 = 0\)
\((x - 1)(x + 4) = 0\)
\(x = (1, -4)\)