Simultaneous Equations
A pair of "Simultaneous equations" is two equations which are both true at the same time. You have two equations which have two unknowns to be found.
Methods
- Method 1- Elimination
- Method 2 - Substitution
Example of simultaneous Equations Using both the methods
- 3f + 2c = 280 (1)
f + 4c = 260 (2)
Substitution Method
= f + 4c - 4c = 260 - 4c = f = 260 - 4c
= 3( 260 - 4c ) + 2c = 280 = 780 - 12c + 2c = 280 = 780 - 10c = 280 = 780 - 10c - 780 = 280 - 780 = -10c = -500 = C = 50
= f = 260 - 4( 50 ) = f = 260 - 200 = f = 60 ∴ F = 60 C = 50 |
Elemination method
= -3( f + 4c = 260 ) = -3f + -12c = -780
= (-3f + -12c = -780) + (3f + 2c = 280) = -10c + -500 = c = 50
= 3f + 2(50) = 280 = 3f + 100 = 280 = 3f +100 - 100 = 280 - 100 = 3f = 180 = f = 60 ∴ F = 60 C = 50 |
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