| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting general conic |
| Difficulty | Moderate -0.5 This is a standard C1 simultaneous equations question involving a line and conic. The method is routine: substitute the linear equation into the quadratic, expand to get a quadratic in one variable, solve, then back-substitute. The arithmetic is straightforward with integer solutions, making it slightly easier than average but still requiring multiple steps. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02f Solve quadratic equations: including in a function of unknown |
5. Find the pairs of values $( x , y )$ which satisfy the simultaneous equations
$$\begin{aligned}
& 3 x ^ { 2 } + y ^ { 2 } = 21 \\
& 5 x + y = 7
\end{aligned}$$
\hfill \mbox{\textit{OCR C1 Q5 [7]}}