Simultaneous Equations with 3 Variables Flashcards

All 4 cards in this deck

What are the steps to solve three linear equations in three unknowns by elimination?

e.g. $x+y+z=6$, $2x+y-z=1$, $x-y+z=2$

1. Eliminate the same unknown from two different pairs: adding gives $3x+2y=7$ and $3x=3$
2. Solve those two equations in two unknowns: $x=1$, $y=2$
3. Substitute both into an original equation: $z=3$

True or false? When solving three equations in three unknowns, it does not matter which unknown you eliminate first.

True. Any of the three may be eliminated first, as long as you eliminate the same one from both pairs.

After the first elimination step with three equations in three unknowns, what should you have?

Two equations containing the same two unknowns, which are then solved as an ordinary simultaneous pair.

How can you check the three values found from three linear equations in three unknowns?

Substitute all three values into each original equation and confirm every one is satisfied.