1MA0 Higher June 2012 Paper 1 Q20
20 Solve the simultaneous equations
\[\begin{aligned} 5x + 2y &= 11 \\ 4x - 3y &= 18 \end{aligned}\](4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(15x + 6y = 33\) \(8x - 6y = 36\) \(23x = 69\) \(5 \times 3 + 2y = 11\) OR \(x = \dfrac{11 - 2y}{5}\) \(4 \times \left(\dfrac{11 - 2y}{5}\right) - 3y = 18\) \(44 - 8y - 15y = 90\) \(-46 = 23y\) \(y = -2\) | \(x = 3\) \(y = -2\) | 4 | M1 for coefficients of \(x\) or \(y\) the same followed by correct operation (condone one arithmetic error) A1 cao for first solution M1 (dep on M1) for correct substitution of found value into one of the equations or appropriate method after starting again (condone one arithmetic error) A1 cao for second solution OR M1 for full method to rearrange and substitute to eliminate \(x\) or \(y\), (condone one arithmetical error) A1 cao for first solution M1 (dep on M1) for correct substitution of found value into one of the equations or appropriate method after starting again (condone one arithmetic error) A1 cao for second solution Trial and improvement 0 marks unless both \(x\) and \(y\) correct values found |