Higher November 2020 Paper 1R Q12
12 Solve the simultaneous equations
\[\begin{aligned} 7x + 2y &= 5.5\\ 3x - 5y &= 17 \end{aligned}\]Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
e.g. \(\begin{aligned} 35x + 10y &= 27.5\\ \underline{\;6x - 10y} &\underline{\;= 34\;}\\ 41x \phantom{{}-10y} &= 61.5 \end{aligned}\) or \(\begin{aligned} 21x + 6y &= 16.5\\ \underline{21x - 35y} &\underline{\;= 119\;}\\ 41y &= -102.5 \end{aligned}\) e.g. \(3x - 5\left(\dfrac{5.5 - 7x}{2}\right) = 17\) or \(7\left(\dfrac{17 + 5y}{3}\right) + 2y = 5.5\) oe | M1 |
| \(x = 1.5\) or \(y = -2.5\) | A1 |
| M1 | |
| Working required Answer: \(x = 1.5\) and \(y = -2.5\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct method to eliminate \(x\) or \(y\):
coefficients of \(x\) or \(y\) the same and correct operator 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.
A1: oe, dep on M1
M1: (dep on 1st M1) for a correct method to find other variable by substitution of found variable into one equation
or for repeating the above method to find the second variable.
A1: oe, dep on M1