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