Edexcel Mathematics (4XMAF) -Unit 2 - 2.6 Simultaneous Linear Equations- Study Notes- New Syllabus
Edexcel Mathematics (4XMAF) -Unit 2 – 2.6 Simultaneous Linear Equations- Study Notes- New syllabus
Edexcel Mathematics (4XMAF) -Unit 2 – 2.6 Simultaneous Linear Equations- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A calculate the exact solution of two simultaneous equations in two unknowns
x + y = 14, x − y = 2
2a + 5b = 12, 3a + b = 5
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Simultaneous Linear Equations
Simultaneous equations are two equations with the same unknowns.
We find values that satisfy both equations at the same time.
Main Method: Elimination
We add or subtract the equations to remove one variable.
Example Given
\( x + y = 14 \)
\( x – y = 2 \)
Add equations:
\( 2x = 16 \Rightarrow x = 8 \)
Substitute into first equation:
\( 8 + y = 14 \Rightarrow y = 6 \)
Solution: \( x = 8, y = 6 \)
Example 1:
Solve:
\( 2a + 5b = 12 \)
\( 3a + b = 5 \)
▶️ Answer/Explanation
Make \( b \) equal:
Multiply second equation by 5:
\( 15a + 5b = 25 \)
Subtract first equation:
\( (15a+5b) – (2a+5b) = 25 – 12 \)
\( 13a = 13 \Rightarrow a = 1 \)
Substitute into \( 3a + b = 5 \):
\( 3(1) + b = 5 \Rightarrow b = 2 \)
Conclusion: \( a = 1, b = 2 \).
Example 2:
Solve:
\( x + y = 9 \)
\( x – y = 5 \)
▶️ Answer/Explanation
Add equations:
\( 2x = 14 \Rightarrow x = 7 \)
Substitute:
\( 7 + y = 9 \Rightarrow y = 2 \)
Conclusion: \( x = 7, y = 2 \).
Example 3:
Solve:
\( 4x + y = 11 \)
\( 4x – y = 3 \)
▶️ Answer/Explanation
Add equations:
\( 8x = 14 \Rightarrow x = \dfrac{14}{8} = \dfrac{7}{4} \)
Substitute:
\( 4(\dfrac{7}{4}) + y = 11 \Rightarrow 7 + y = 11 \Rightarrow y = 4 \)
Conclusion: \( x = \dfrac{7}{4}, y = 4 \).