Foundation January 2022 Paper 2 Q25
25 Solve the simultaneous equations
\(3x + 5y = 3.1\)
\(6x + 3y = 3.75\)
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
eg \(\begin{aligned} 6x + 10y &= 6.2 \\ \underline{6x + 3y} &\underline{\;= 3.75} \\ 7y &= 2.45 \end{aligned}\) eg \(\begin{aligned} 30x + 15y &= 18.75 \\ \underline{9x + 15y} &\underline{\;= 9.3} \\ 21x &= 9.45 \end{aligned}\) or eg \(6\left(\dfrac{3.1 - 5y}{3}\right) + 3y = 3.75\) | M1 |
| eg. 6 × “0.45” + \(3y\) = 3.75 or 3 × “0.45” + \(5y\) = 3.1 or \(3x\) + 5 × “0.35” = 3.1 or \(6x\) + 3 × “0.35” = 3.75 | M1 |
| Working required Answer: \(x = 0.45\) oe \(y = 0.35\) oe | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for correct method to eliminate one variable – multiplying one or both equations so the coefficient of \(x\) or \(y\) is the same in both (condone one arithmetic error), with the intention to subtract all 3 terms to eliminate one variable (intention to subtract is clearly showing a minus sign or subtracting 2 or 3 out of 3 terms)
or isolating \(x\) or \(y\) in one equation and substituting into the other
M1: dep. Substitute found value into one equation or correct method to eliminate second unknown.
A1: dep M1