Elimination Method - Addition and Subtraction

Idea of elimination

We eliminate one variable by adding or subtracting the equations, then solve for the remaining variable.

When to add

If the coefficients of one variable are equal but opposite in sign, add.

Example:
2x + 3y = 13 -- (1)
4x - 3y = 11 -- (2)
Add (1)+(2): 6x = 24   ⇒   x = 4
Sub into (1): 2(4) + 3y = 13   ⇒   3y = 5   ⇒   y = 5/3

When to subtract

If the coefficients of one variable are equal with same sign, subtract.

Example:
5x + 2y = 16 -- (1)
3x + 2y = 10 -- (2)
(1)-(2): 2x = 6   ⇒   x = 3
Sub into (2): 3(3) + 2y = 10   ⇒   2y = 1   ⇒   y = 1/2

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