AQA · Mathematics · 8300
GCSE Maths: Simultaneous equations (advanced)
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Simultaneous equations (advanced) (Corbettmaths Video 298), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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When solving simultaneous equations with one linear and one quadratic equation, which equation should you typically substitute into the other?
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Substitute the linear equation (already solved for one variable, or easy to solve) into the quadratic equation.
How many solutions can a system of one linear and one quadratic equation have?
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Zero, one, or two solutions, depending on whether the line misses, is tangent to, or intersects the curve.
How can you prove a line is tangent to a curve using simultaneous equations?
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Solve the simultaneous equations; if the discriminant equals zero (or there is exactly one repeated solution), the line is tangent to the curve.
What geometric relationship do simultaneous equations represent when one is linear and one is quadratic?
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The intersection points of a straight line and a curve (such as a parabola or circle).
When solving x² + y² = 13 and x + y = 5, what type of curve does the first equation represent?
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A circle centered at the origin with radius √13.
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