Additional Mathematics – Simultaneous equations | e-Consult
Simultaneous equations (1 questions)
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From the second equation, \(y = x - 1\).
Substitute into the first:
\(x^{2} + (x - 1) = 7 \;\Rightarrow\; x^{2} + x - 1 = 7\)
\(x^{2} + x - 8 = 0\)
Factorising:
\((x + 4)(x - 2) = 0\)
Hence \(x = 2\) or \(x = -4\).
Corresponding \(y\) values:
- If \(x = 2\), then \(y = 2 - 1 = 1\).
- If \(x = -4\), then \(y = -4 - 1 = -5\).
Therefore the system has two solutions: \((x, y) = (2, 1)\) and \((x, y) = (-4, -5)\).