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AdvancedMaths revision

Simultaneous Equations (Advanced)

Solve systems where linear and non-linear constraints intersect.

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Focus points
✓Solve line-curve systems.
✓Recognise multiple intersections.
✓Use substitution without losing solutions.
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The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · line-circle system
Solve y=x+1 and x²+y²=25.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · line-parabola system
Solve y=x²−4 and y=2x+5.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · sum-product system
Solve xy=12 and x+y=7.
Question 4FluencyCore
Original practice · Free Online Revision
Skill · non-linear system
Solve x²+y²=34 and x−y=2.
Question 5ReasoningCore
Original practice · Free Online Revision
Skill · intersection count
How many intersections do y=x² and y=2x−2 have?
Question 6ApplicationCore
Original practice · Free Online Revision
Skill · modelling
A rectangle has perimeter 26 cm and area 40 cm². Find its side lengths.
Question 7ReasoningStretch
Original practice · Free Online Revision
Skill · tangency parameter
Find k so y=x² and y=4x+k touch at exactly one point.
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · symmetric system
Solve x+y=1 and x³+y³=7.