Foundation June 2023 Paper 1 Q24
24 Solve the simultaneous equations
\(\begin{aligned} 2x + 9y &= 14.5 \\ 7x + 3y &= 8 \end{aligned}\)
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
eg \(\begin{aligned} 21x + 9y &= 24 \quad - \\ 2x + 9y &= 14.5 \end{aligned}\) or \(\begin{aligned} 14x + 63y &= 101.5 \quad - \\ 14x + 6y &= 16 \end{aligned}\) or eg \(7 \times \left(\dfrac{14.5 - 9y}{2}\right) + 3y = 8\) | M1 |
| M1 | |
| Working required Answer: \(x = 0.5\) and \(y = 1.5\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct method to eliminate \(x\) or \(y\):
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, dep on M1