Specimen 2020 Paper 1 Q17
17 Solve the simultaneous equations
\[\begin{aligned} 2a + b - c &= 8 \\ 4a - 3b - 2c &= -9 \\ 6a + 3b + c &= 0 \end{aligned}\][5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Correct attempt to eliminate two variables from left hand side | M1 | eg \(2(2a + b - c) - (4a - 3b - 2c)\) |
| Correct attempt to eliminate two variables | M1dep | eg \(2(2a + b - c) - (4a - 3b - 2c)\) \(= 2 \times 8 - (-9)\) or \(5b = 25\) |
| Solves their equation | M1dep | eg \(b = 25 \div 5\) or \(b = 5\) |
| Substitutes their value into two equations and correct method to eliminate a variable | M1 | eg \(2a + 5 - c = 8\) and \(6a + 15 + c = 0\) and \(8a + 20 = 8\) |
| \(a = -\dfrac{3}{2}\) and \(b = 5\) and \(c = -6\) | A1 | oe |
| Alternative method 2 | ||
| Two correct attempts to eliminate same variable from left hand side | M1 | eg \(3(2a + b - c) + (4a - 3b - 2c)\) and \(4a - 3b - 2c + 6a + 3b + c\) |
| Two correct attempts to eliminate same variable | M1dep | eg \(3(2a + b - c) + (4a - 3b - 2c)\) \(= 24 - 9\) and \(4a - 3b - 2c + 6a + 3b + c = 0 - 9\) or \(10a - 5c = 15\) and \(10a - c = -9\) |
| Correct attempt to eliminate a variable from their two equations | M1dep | eg \(10a - 5c - (10a - c) = 15 - 9\) or \(-4c = 24\) or \(c = -6\) |
| Substitutes their value into two equations and correct method to eliminate a variable | M1 | eg \(2a + b + 6 = 8\) and \(4a - 3b + 12 = -9\) and \(2(2a + b + 6) - (4a - 3b + 12)\) \(= 2 \times 8 - (-9)\) |
| \(a = -\dfrac{3}{2}\) and \(b = 5\) and \(c = -6\) | A1 | oe |