Elimination Method - JSS3 Mathematics Lesson Note

The elimination method involves eliminating one of the variables by adding or subtracting the equations together. Here is how it works:

Example:

Consider the equations:

2𝑥+3𝑦=8

4𝑥−2𝑦=2

Step 1: Multiply the equations if necessary to make the coefficients of one variable opposites.

Multiply the first equation by 2:

4𝑥+6𝑦=16

Step 2: Subtract the modified equation from the second original equation:

(4𝑥+6𝑦)−(4𝑥−2𝑦)=16−2

8𝑦=14

Step 3: Solve for 𝑦:

𝑦=14/8=1.75

Step 4: Substitute 𝑦 back into one of the original equations to find 𝑥:

2𝑥+3(1.75)=8

2𝑥+5.25=8

2𝑥=8−5.25

2𝑥=2.75

𝑥=2.75/2=1.375

Therefore, 𝑥=1.375 and 𝑦=1.75 are the solutions.