Foundation January 2023 Paper 1R Q21
21 Solve the simultaneous equations
\[\begin{aligned} x + 2y &= 15 \\ 4x - 6y &= 4 \end{aligned}\]Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
eg \(\begin{aligned} 4x + 8y &= 60 \\ -\;\; 4x - 6y &= 4 \end{aligned}\) (\(14y = 56\)) or \(\begin{aligned} 3x + 6y &= 45 \\ +\;\; 4x - 6y &= 4 \end{aligned}\) (\(7x = 49\)) eg \(4x - 6\left(\dfrac{15 - x}{2}\right) = 4\) or \(4(15 - 2y) - 6y = 4\) oe | M1 |
| eg \(x + 2 \times 4 = 15\) or \(7 + 2 \times y = 15\) | M1 |
| Working required Answer: \(x = 7\), \(y = 4\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: 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 correctly 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.
A1: dep on M1