Simultaneous Equation for all Students Across the World

Simultaneous Linear Equations: The Complete Guide for WAEC, NECO, & JAMB

Master simultaneous linear equations for top exam marks with this comprehensive guide, covering elimination, substitution, word problems, fractions, and indices.

1. The Elimination Method

Eliminate variables by adding/subtracting equations.

2x + 3y = 12
2x - y = 4

1. Subtract equations to eliminate x: 4y = 8 → y = 2

2. Substitute y back: 2x + 3(2) = 12 → x = 3

Result: x = 3, y = 2

2. The Substitution Method

Isolate one variable and substitute it into the other equation.

y = 3x - 1
2x + y = 14

1. Substitute y: 2x + (3x - 1) = 14 → 5x = 15 → x = 3

2. Find y: y = 3(3) - 1 → y = 8

Result: x = 3, y = 8

3. Word Problems (WAEC Style)

Translate problems: 3t + 2n = 12,000 and 2t + 4n = 10,000.

Scaling & subtracting reveals: Textbook (t) = ₦3,500, Notebook (n) = ₦750.

4. Fractional Systems (JAMB Style)

Clear fractions using the Least Common Multiple (LCM).

x/2 + y/3 = 4
x - y = 3

Multiply Eq 1 by 6: 3x + 2y = 24. Solve using substitution. Result: x = 6, y = 3.

5. Exponential Base Method

Strip matching bases: 3^(x+y)=27 → x+y=3; 2^(2x-y)=8 → 2x-y=3.

Add equations: 3x = 6 → x=2. Result: x = 2, y = 1.