4. Solve the simultaneous equations
$$\begin{gathered}
x + y = 2 \\
x ^ { 2 } + 2 y = 12
\end{gathered}$$
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Answer Marks
Guidance
\(x^2 + 2(2-x) = 12\) or \((2-y)^2 + 2y = 12\) (Eqn. in \(x\) or \(y\) only) M1
\(x^2 - 2x - 8 = 0\) or \(y^2 - 2y - 8 = 0\) (Correct 3 term version) A1
\((x-4)(x+2) = 0\) \(x = \ldots\) or \((y-4)(y+2) = 0\) \(y = \ldots\) M1
\(x = 4, x = -2\) or \(y = 4, y = -2\) A1
\(y = -2, y = 4\) or \(x = -2, x = 4\) (M: attempt one, A: both) M1 A1ft
(6 marks)
Total: 6 marks Non-algebraic solutions:
Answer Marks
No working, and only one correct solution pair found (e.g. \(x = 4, y = -2\)): M0 A0 M0 A0 M1 A1
No working, and both correct solution pairs found, but not demonstrated: M0 A0 M1 A1 M1 A1
Both correct solution pairs found, and demonstrated, perhaps in a table of values: Full marks
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$x^2 + 2(2-x) = 12$ or $(2-y)^2 + 2y = 12$ (Eqn. in $x$ or $y$ only) | M1 |
$x^2 - 2x - 8 = 0$ or $y^2 - 2y - 8 = 0$ (Correct 3 term version) | A1 |
$(x-4)(x+2) = 0$ $x = \ldots$ or $(y-4)(y+2) = 0$ $y = \ldots$ | M1 |
$x = 4, x = -2$ or $y = 4, y = -2$ | A1 |
$y = -2, y = 4$ or $x = -2, x = 4$ (M: attempt one, A: both) | M1 A1ft | (6 marks)
**Total: 6 marks**
**Non-algebraic solutions:**
No working, and only one correct solution pair found (e.g. $x = 4, y = -2$): | M0 A0 M0 A0 M1 A1 |
No working, and both correct solution pairs found, but not demonstrated: | M0 A0 M1 A1 M1 A1 |
Both correct solution pairs found, and demonstrated, perhaps in a table of values: | Full marks |
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4. Solve the simultaneous equations
$$\begin{gathered}
x + y = 2 \\
x ^ { 2 } + 2 y = 12
\end{gathered}$$
\hfill \mbox{\textit{Edexcel C1 2005 Q4 [6]}}