Graphing requires you evaluate the equations at least twice. It can get you close to the answer, but may not give you an exact answer.

Substitution requires you solve at least one of the equations for one of the variables, and the result of doing the substitution may require further simplification steps.

Elimination requires finding a set of coefficients for multiplying the equations. It is conveniently used when the numbers are obvious and/or small. Sometimes it requires the equations be rearranged. In the end, it is usually about the same amount of work as substitution.

Cramer's rule can provide a solution to equations in standard form quite easily. Sometimes the exercise of keeping the signs straight is more trouble than it is worth. Often, funny large numbers are obtained, even though the result is simple small numbers. Explaining this method to someone else is difficult.

I usually prefer substitution or elimination for 2-variable linear equations. I pick what seems to be the easiest at the time. I sometimes use graphing for polynomials or trig equations, just to see what the functions look like.

Substitution requires you solve at least one of the equations for one of the variables, and the result of doing the substitution may require further simplification steps.

Elimination requires finding a set of coefficients for multiplying the equations. It is conveniently used when the numbers are obvious and/or small. Sometimes it requires the equations be rearranged. In the end, it is usually about the same amount of work as substitution.

Cramer's rule can provide a solution to equations in standard form quite easily. Sometimes the exercise of keeping the signs straight is more trouble than it is worth. Often, funny large numbers are obtained, even though the result is simple small numbers. Explaining this method to someone else is difficult.

I usually prefer substitution or elimination for 2-variable linear equations. I pick what seems to be the easiest at the time. I sometimes use graphing for polynomials or trig equations, just to see what the functions look like.