2026 NASS P2 Q1

2026 NASS P2 Q1

Secondary 4
5 marks

The simultaneous equations \(y=x^2+px-6\) and \(y=2x+\dfrac32\) have a common solution for which \(x=3\). Find the value of \(p\), and hence solve the simultaneous equations.[5]

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Answer:\(p=\dfrac32\); \((x,y)=\left(3,\dfrac{15}2\right)\) or \(\left(-\dfrac52,-\dfrac72\right)\).

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