Higher November 2020 Paper 1 Q18
18 Solve the simultaneous equations
\[\begin{aligned} 2x + 4y &= -9 \\ 2y &= 4x - 7 \end{aligned}\][4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: substitutes for \(4y\) in first equation then substitutes value of \(x\) | ||
| \(2x + 2(4x - 7) = -9\) or \(10x = 5\) | M1 | oe correct elimination of \(y\) |
| \((x =)\ \dfrac{1}{2}\) or \((x =)\ 0.5\) | A1 | oe eg \((x =)\ \dfrac{5}{10}\) |
| \(2 \times\) their \(\dfrac{1}{2} + 4y = -9\) or \(2y = 4 \times\) their \(\dfrac{1}{2} - 7\) | M1dep | oe substitution of their \(x\) into either equation |
| \((y =)\ {-}\dfrac{5}{2}\) or \((y =)\ {-}2\dfrac{1}{2}\) or \((y =)\ {-}2.5\) | A1 | oe eg \((y =)\ {-}\dfrac{10}{4}\) |
| Alternative method 2: equates coefficients | ||
| Equates coefficients for one unknown and if necessary, rearranges into appropriate form and adds or subtracts equations appropriately | M1 | eg 1 changes 1st equation to \(4x + 8y = -18\), rearranges 2nd equation to \(2y - 4x = -7\) and adds to eliminate \(x\) eg 2 changes 2nd equation to \(4y = 8x - 14\) and subtracts to eliminate \(y\) |
| Correct value for \(x\) or \(y\) | A1 | |
| Substitutes their value into an equation | M1dep | |
| Both values correct | A1 | |
| Alternative method 3: substitutes for \(4x\) in second equation then substitutes value of \(y\) | ||
| \(2y = 2(-9 - 4y) - 7\) or \(10y = -25\) | M1 | oe correct elimination of \(x\) |
| \((y =)\ {-}\dfrac{5}{2}\) or \((y =)\ {-}2\dfrac{1}{2}\) or \((y =)\ {-}2.5\) | A1 | oe eg \((y =)\ {-}\dfrac{25}{10}\) |
| \(2x + 4 \times\) their \(-\dfrac{5}{2} = -9\) or \(2 \times\) their \(-\dfrac{5}{2} = 4x - 7\) | M1dep | oe substitution of their \(y\) into either equation |
| \((x =)\ \dfrac{1}{2}\) or \((x =)\ 0.5\) | A1 | oe eg \((x =)\ \dfrac{2}{4}\) |
| Alternative method 4: solves each unknown separately - substitutes for \(4y\) in first equation then substitutes for \(4x\) in second equation | ||
| \(2x + 2(4x - 7) = -9\) or \(10x = 5\) | M1 | oe correct elimination of \(y\) |
| \((x =)\ \dfrac{1}{2}\) or \((x =)\ 0.5\) | A1 | oe eg \((x =)\ \dfrac{5}{10}\) |
| \(2y = 2(-9 - 4y) - 7\) or \(10y = -25\) | M1 | oe elimination of \(x\) |
| \((y =)\ {-}\dfrac{5}{2}\) or \((y =)\ {-}2\dfrac{1}{2}\) or \((y =)\ {-}2.5\) | A1 | oe eg \((y =)\ {-}\dfrac{25}{10}\) |
Additional guidance
| Note that in alt 4 the 2nd M mark is not dependent | |
| In alt 4, allow alt 2 method for each unknown | |
| Both answers correct | M1A1M1A1 |