Foundation January 2023 Paper 2 Q22
22 Solve the simultaneous equations
\[\begin{aligned} 5x + 4y &= -2 \\ 2x - y &= 4.4 \end{aligned}\]Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
eg \(\begin{aligned} 5x + 4y &= -2 \\ +\;\; 8x - 4y &= 17.6 \end{aligned}\) (\(13x = 15.6\)) eg \(\left[x = \dfrac{4.4 + y}{2}\right]\) oe \(5\left(\dfrac{4.4 + y}{2}\right) + 4y = -2\) oe or eg \(\begin{aligned} 10x + 8y &= -4 \\ -\;\; 10x - 5y &= 22 \end{aligned}\) (\(13y = -26\)) eg \([y = 2x - 4.4]\) oe \(5x + 4(2x - 4.4) = -2\) oe | M1 |
| eg \(5 \times \text{“}1.2\text{”} + 4y = -2\) or \(2 \times \text{“}1.2\text{”} - y = 4.4\) or eg \(5x + 4 \times \text{“}{-2}\text{”} = 4.4\) or \(2x - \text{“}{-2}\text{”} = 4.4\) | M1 |
| Working required Answer: \(x = 1.2\) \(y = -2\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: multiplication of one or both equation(s) with correct operation selected (allow one arithmetic error) (if + or – is not shown then assume it is the operation that at least 2 of the 3 terms have been calculated for)
or
correct rearrangement of one equation with substitution into second
M1: (dep on previous M1 but not on a correct first value) correct method to find second unknown – this could be a correct substitution into one of the equations given or calculated or starting again with the same style of working as for the first method mark
A1: oe eg \(x = \dfrac{6}{5}\)
for both solutions dependent on first M1