LESSON 4 – THE METHOD OF ELIMINATION
RECALL

Multiplying/Dividing both sides of an equation by a constant does not change the equation.
Ex:

2𝑥 − 4𝑦 = −12 can be written as:
Adding and subtracting two equations forms a new equation but does not change the solution.
Ex:
𝑥 − 2𝑦 = 8
𝑥 − 2𝑦 = 8
+ 𝑥 + 3𝑦 = 4
– 𝑥 + 3𝑦 = 4
SOLVING BY ELIMINATION
 Ensure both equations are written in the form 𝑎𝑥 + 𝑏𝑦 = 𝑐
 Eliminate one of the variables by adding or subtracting the equations.
ELIMINATING A VARIABLE

Look for the variable that has the same coefficient in both equations
Example
Which variable would you choose to eliminate?
2𝑥 − 3𝑦 = 10
5𝑥 + 3𝑦 = 4

−2𝑥 − 5𝑦 = 2
−2𝑥 + 5𝑦 = 4
If neither variable has the same coefficient, multiply or divide one or both equations by a
constant.
4𝑥 + 8𝑦 = 7
−5𝑥 + 2𝑦 = −10
5𝑥 + 3𝑦 = −2
−2𝑥 − 7𝑦 = 1
Example ① −3𝑥 + 4𝑦 = 7
3𝑥 + 𝑦 = −2
Example ②
3𝑥 + 2𝑦 – 13 = 0
−2𝑥 + 4𝑦 – 2 = 0
Example ③
3𝑥 − 2𝑦 = 2
−10𝑥 + 3𝑦 = 8