Solve the following pair of linear equations by the substitution method:
$x + y = 14$
$x - y = 4$
Step-by-Step Solution
Key Concept: Express $x$ from one equation ($x = y + 4$) and substitute into the other.
Stepwise Solution:
From second equation: $x = y + 4$. Substitute into first equation: $(y + 4) + y = 14$. [1.0 Mark]
$2y + 4 = 14 \Rightarrow 2y = 10 \Rightarrow y = 5$.
Then $x = 5 + 4 = 9$. Solution is $x = 9, y = 5$. [1.0 Mark]
Marking Scheme:
• Expressing $x$ in terms of $y$ and substituting: 1.0 Mark
• Correct values of $x = 9, y = 5$: 1.0 Mark
Correct Answer: