Question on: SS2 Mathematics - Simultaneous Linear and Quadratic Equations
Solve the simultaneous equations \(3x + y = 10\) and \({2x}^{2} + y^{2} = 19\).
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1. **Express y in terms of x from the linear equation:**
From \(3x + y = 10\), we get \(y = 10 - 3x\).
2. **Substitute y into the quadratic equation:**
Substitute \(y = 10 - 3x\) into \(2x^2 + y^2 = 19\):
\(2x^2 + (10 - 3x)^2 = 19\)
3. **Expand and simplify the quadratic equation:**
\(2x^2 + (100 - 60x + 9x^2) = 19\)
\(11x^2 - 60x + 100 =
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