4MA0 Higher June 2014 Paper 3R Q13
13 Solve the simultaneous equations \[\begin{aligned} 3x + 4y &= 6 \\ 5x + 6y &= 11 \end{aligned}\]
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
Eg. \(\begin{aligned} 15x + 20y &= 30 \\ 15x + 18y &= 33 \end{aligned}\) or \(\begin{aligned} 18x + 24y &= 36 \\ 20x + 24y &= 44 \end{aligned}\) oe or \(3x + 4\left(\dfrac{11 - 5x}{6}\right) = 6\) oe or \(3\left(\dfrac{11 - 6y}{5}\right) + 4y = 6\) oe | M1 |
| \(y = -1\frac{1}{2}\) or \(x = 4\) | A1 |
| Eg. 3x + 4(−1.5) = 6 oe | M1 |
| \(x = 4,\; y = -1\frac{1}{2}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: For coefficient of \(x\) or \(y\) the same and correct operation to eliminate selected one (condone any one arithmetic error in multiplication)
or
For correct rearrangement of one equation followed by correct substitution in the other.
A1: Cao dep on M1
M1: (dep on 1st M1) for substituting the other variable
A1: Award 4 marks for correct values if at least first M1 scored