Line intersecting quadratic curve

A question is this type if and only if it asks to find intersection points of a straight line with a parabola or quadratic curve (y = ax² + bx + c form).

29 questions · Moderate -0.5

1.02c Simultaneous equations: two variables by elimination and substitution
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Edexcel C1 Q4
6 marks Moderate -0.3
Solve the simultaneous equations $$x + y = 2$$ $$x^2 + 2y = 12.$$ [6]
Edexcel C1 Specimen Q6
9 marks Moderate -0.8
  1. Solve the simultaneous equations $$y + 2x = 5,$$ $$2x^2 - 3x - y = 16.$$ [6]
  2. Hence, or otherwise, find the set of values of \(x\) for which $$2x^2 - 3x - 16 > 5 - 2x$$ [3]
Edexcel C1 Q4
7 marks Moderate -0.3
Find the pairs of values \((x, y)\) which satisfy the simultaneous equations $$3x^2 + y^2 = 21$$ $$5x + y = 7$$ [7]
OCR MEI Paper 2 Specimen Q1
5 marks Moderate -0.8
In this question you must show detailed reasoning. Find the coordinates of the points of intersection of the curve \(y = x^2 + x\) and the line \(2x + y = 4\). [5]