Foundation June 2018 Paper 2 Q23
23 Solve the simultaneous equations\[\begin{aligned} x + y &= 15 \\ 7x - 5y &= 3 \end{aligned}\]Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
| eg \(\begin{aligned} 7x + 7y &= 105 \;\; - \\ 7x - 5y &= 3 \end{aligned}\) or \(\begin{aligned} 5x + 5y &= 75 \;\; + \\ 7x - 5y &= 3 \end{aligned}\) or \(7(15 - y) - 5y = 3\) or \(7x - 5(15 - x) = 3\) oe | M1 |
| \(6.5 + y = 15\) or \(x + 8.5 = 15\) or \(7 \times 6.5 - 5y = 3\) or \(7x - 5 \times 8.5 = 3\) | M1 |
| Working required Answer: \(x = 6.5\), \(y = 8.5\) | A1oe |
| (3) | |
| (3 marks) |
Notes
M1: Correct method to eliminate \(x\) or \(y\): coefficients of \(x\) or \(y\) the same and correct operation to eliminate selected variable (condone any one arithmetic error in multiplication) or writing \(x\) or \(y\) in terms of the other variable and correctly substituting
M1: dep Correct method to find second variable using their value from a correct method to find first variable or for repeating above method to find second variable
A1oe: dep on first M1