4400 Higher June 2009 Paper 3 Q11
11
(a) Solve the simultaneous equations\[\begin{aligned} 2x - 3y &= 9 \\ 5x + 4y &= 11 \end{aligned}\] (4)
(b) Write down the coordinates of the point of intersection of the two lines whose equations are \(2x - 3y = 9\) and \(5x + 4y = 11\) (1)
| Scheme | Marks |
|---|---|
| \(10x - 15y = 45\) \(10x + 8y = 22\) or \(8x - 12y = 36\) \(15x + 12y = 33\) | M1 |
| \(y = -1\) or \(x = 3\) | A1 |
| M1 | |
| \(x = 3\), \(y = -1\) | A1 |
| (4) |
Notes
M1: for coefficients of \(x\) or \(y\) the same followed by correct operation
or for correct rearrangement of one equation followed by substitution in the other eg \(5x + 4\left(\dfrac{2x - 9}{3}\right) = 11\)
For both approaches, condone one arithmetical error
A1: cao dep on M1
M1: (dep on 1st M1) for substituting for other variable
A1: cao dep on all preceding marks
| Scheme | Marks |
|---|---|
| (3, \(-1\)) | B1 |
| (1) | |
| (5 marks) |
Notes
B1: ft from (a)