How do you know what method to use when solving a system of equations?

Answer 1

For 2 x 2 systems....

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if any of the vars do not have a number in front of it,

then it's COEFFICIENT is 1. That system is best

solved using substitution method. You solve that equation

for the variable that is ALONE (with no number in front, coefficient is 1)

and then substitute THAT new expression into the other equation.

Otherwise, elimination is the better strategy.

Ex. 2x + 3y = 8 vs 3x - y = 7 <---- substitution

Ex. 3x-4y = 9 vs. 2x + 3y = 5 <--- elimination

For 4x4 systems or larger, Guassian Elimination is

the better strategy if there are A LOT of coefficients

that are not 1 or zero. Otherwise, your matrix will

be SPARSE

For 3 x 3:

First select which variable is best to eliminate.

Pair the 1st two equations, and eliminate the variable as if it were 2x2

Pair the 2nd and 3rd equations and eliminate the SAME variable as if they were 2x2

You will then get a 2x2 system, which can be solved via elimination or substitution