CORE_MATH • SHS 1Term 2WAEC / WASSCE SyllabusVIP Lesson
Simultaneous Linear Equations
Elimination method, substitution method, graphical intersection method, and practical commercial word problems.
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Real-World Context & Relevance in Ghana
A bakery in Takoradi producing loaves of bread and meat pies determines individual ingredient costs by tracking daily flour and butter purchases across two distinct batch days.
Key Syllabus Learning Objectives
- 1Solve 2×2 systems of linear equations using the elimination method
- 2Solve systems using the substitution method efficiently
- 3Interpret simultaneous solutions graphically as intersection points of lines
- 4Formulate and solve real-world commercial word problems
1
The Elimination Strategy
Align equations in the standard form ax + by = c. Decide which variable to eliminate. If coefficients have the same sign, subtract the equations. If coefficients have opposite signs, add them.
- Arrange equations: a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
- Multiply to balance coefficients.
- Same sign -> Subtract; Opposite sign -> Add.
- Substitute the found variable back into any original equation.
Core Takeaway:
Check both solutions in BOTH original equations to ensure accuracy.
WAEC / WASSCE Examiner Tips
- Clearly label your equations as (1) and (2) and write down the operation performed (e.g. "Subtract (2) from (1)").
- Do not forget to find the second variable; many candidates find x and forget y, losing half the marks.
- In word problems, translate prices or quantities into words before concluding.
Common Candidate Pitfalls & Errors to Avoid
- Subtracting equations incorrectly when negative signs are involved.
- Substituting the expression back into the same equation it was derived from when using substitution.
- Finding only one variable instead of both.
Topic Mastery Checklist
- Can I balance coefficients to eliminate x or y?
- Can I use substitution when one variable has a coefficient of 1?
- Can I translate a two-item shopping problem into simultaneous equations?
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