CAIE A-Level Mathematics 1.1.4 Simultaneous Linear and Quadratic Equations

CAIE A-Level Mathematics 1.1.4 Simultaneous Linear and Quadratic Equations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise substituting a linear equation into a quadratic relation, solving the resulting quadratic and pairing both coordinates for every valid intersection.

How this is tested

  • rearrange the linear equation and substitute it into the quadratic relation without losing terms
  • solve the resulting three-term quadratic and back-substitute each root for its paired coordinate

Question 2

[Maximum number: 4]

Find the coordinates of the points of intersection of the curve and the line with equations

2xy+5y2=24 and 2x+y+4=0.2 x y+5 y^{2}=24 \text { and } 2 x+y+4=0 .