4MA0 Higher January 2014 Paper 3R Q13
13
(a) Solve the simultaneous equations \[\begin{aligned} 3x + 5y &= 14 \\ 4x + 3y &= 4 \end{aligned}\] Show clear algebraic working. (4)
(b) Write down the coordinates of the point of intersection of the two lines whose equations are \(3x + 5y = 14\) and \(4x + 3y = 4\) (1)
| Scheme | Marks |
|---|---|
| \(12x + 20y = 56\) \(12x + 9y = 12\) or \(9x + 15y = 42\) \(20x + 15y = 20\) | M1 |
| (\(y\) =) 4 or (\(x\) =) −2 | A1 |
| eg \(3x + 5 \times 3 = 14\) | M1 |
| −2 4 | A1 |
| (4) |
Notes
M1: for coefficients of \(x\) or \(y\) the same or for correct rearrangement of one equation followed by substitution in the other eg \(3x + 5\left(\dfrac{4 - 4x}{3}\right) = 14\)
A1: dep on M1
M1: (dep on first M1) for substituting for the other variable
A1: cao dep Award full marks for correct values if at least first M1 scored
The mark scheme states that for this question the correct answer alone does not imply a correct method.
| Scheme | Marks |
|---|---|
| −2, 4 | B1 |
| (1) | |
| (5 marks) |
Notes
B1: ft from (a)