Higher November 2023 Paper 3 Q11
11 Solve these simultaneous equations. [3 marks]
\(7x + 2y = 100\)
\(3x + 2y = 48\)
| Answer | Mark | Comments |
|---|---|---|
| Any correct method that would lead to an equation in \(x\) or an equation in \(y\) | M1 | eg \(7x - 3x = 100 - 48\) or \(100 - 7x = 48 - 3x\) or \(7x + 2\left(\dfrac{48 - 3x}{2}\right) = 100\) or \(3x + 2\left(\dfrac{100 - 7x}{2}\right) = 48\) or \(4x = 52\) or \(14y - 6y = 336 - 300\) or \(7\left(\dfrac{48 - 2y}{3}\right) + 2y = 100\) or \(3\left(\dfrac{100 - 2y}{7}\right) + 2y = 48\) or \(8y = 36\) |
| \(x = 13\) or \(y = 4.5\) or \(y = 4\dfrac{1}{2}\) or \(y = \dfrac{9}{2}\) | A1 | |
| \(x = 13\) and \(y = 4.5\) or \(y = 4\dfrac{1}{2}\) or \(y = \dfrac{9}{2}\) | A1 |
Additional guidance
| \((7x + 2y) - (3x + 2y) = 100 - 48\) | M1 |
| One correct value with one incorrect value (or no second value) | M1A1A0 |
| Embedded correct values in both equations | M1A1A0 |
| Embedded correct values in one equation only | M1A0A0 |