Foundation June 2017 Paper 1 Q28
28 Solve the simultaneous equations.
\(2x + y = 18\)
\(\;\;x - y = 6\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(2x + x = 18 + 6\) | M1 | oe Eliminates a variable Implied by \(3x = n\), where \(n \gt 18\) |
| \(3x = 24\) or \(x = 8\) | A1 | oe |
| \(x = 8\) and \(y = 2\) | A1 | |
| Alternative method 2 | ||
| \(y - -2y = 18 - 2 \times 6\) or \(y - -2y = 18 - 12\) or \(y + 2y = 18 - 2 \times 6\) or \(y + 2y = 18 - 12\) | M1 | oe Eliminates a variable Implied by \(2x - 2y = 12\) followed by \(3y = m\), where \(m \lt 18\) |
| \(3y = 6\) or \(-3y = -6\) or \(y = 2\) or \(-y = -2\) | A1 | oe |
| \(x = 8\) and \(y = 2\) | A1 | |
| Alternative method 3 | ||
| \(\dfrac{18 - y}{2} = y + 6\) or \(18 - 2x = x - 6\) | M1 | oe Eliminates a variable |
| \(3x = 24\) or \(x = 8\) or \(3y = 6\) or \(y = 2\) | A1 | oe Collects terms |
| \(x = 8\) and \(y = 2\) | A1 | |
| Alternative method 4 | ||
| Correctly evaluated trial of at least one pair of values in one equation for which they do not work | M1 | eg \(9 - 2 = 7\) The pair of values must not be given as the answer |
| Correctly evaluated trial of at least three pairs of values in one equation for which they do not work | M1dep | eg \(9 - 2 = 7\) \(2 \times 11 + 5 = 27\) \(10 - (-2) = 12\) With none of the three pairs of values given as the answer |
| \(x = 8\) and \(y = 2\) | A1 | |
Additional guidance
| One correct value with one incorrect value (or no second value) and no working eg \(\;x = 6\) and \(y = 2\) eg \(\;y = 2\) | M1A1A0 M1A1A0 M1A1A0 |
| (8, 2) or 8, 2 on answer line (with or without working) | M1A1A1 |
| (2, 8) or 2, 8 on answer line with no working | M0A0A0 |
| Embedded, correct values in one equation only eg \(\;2 \times 8 + 2 = 18\) Embedded, correct values in both equations ie \(\;2 \times 8 + 2 = 18\) and \(8 - 2 = 6\) | M1A0A0 M1A1A0 |
| Please check crossed out work, which may indicate correct rejection of a trial in this question, as covered in alternative method 4 |