How can you tell which method to use for a problem when choosing between the substitution method, addition,etc

Answer 1

Generally, you pick the simplest method. For instance, if one of the equations is already in slope-intercept form, it's probably best to use substitution (since you already have y isolated on one side of the equation). If you have a system of linear equations all in standard form, the addition method is the simplest. You don't have to worry too much about choosing the right method though - you'll get the same answer no matter which one you use.

Answer 2

please be a little more specific. which method to use for what type of problem(s)? if you meant problems involving the solution of a simultaneous system of n linear equations in n unknowns, there is a general formula (via Cramer's Rule) for the n variables in terms of the n^2 + n coefficients (i.e. constant terms included). if you want to be a little bit more simple, like you wish to solve a system of 2 linear equations in 2 unknowns, then it would be a matter of inspecting the coefficients of x and y, vis-a-vis:

ax + by = c
dx + ey = f

to determine whether the substitution or addition method would "work". (of course, each method would always work, given the correct conditions.)

for example, if you are given:

5x + 3y = 2
-5x + 6y = 7, then the best method to use here would be the addition method.

otherwise, if you are given something like:

4x - 7y = 127
3x + 13y = 17

then I guess the best method to use here would be either Cramer's Rule for the case n = 2 or the substitution method. (in using the substitution method, just be careful with your arithmetic and signs.)

Answer 3

Substitution method is best when there is an x or y without a coefficient other than 1. Otherwise elimination works best.

Answer 4

we normally use addition method if the coefficients of x or y are the same in the 2 equations.substitution is used if you can make y the subject very easily in 1 equation.

Answer 5

y=3x+6
y=5x-5
This would be a good example of when to use substitution because you already have both equation expressed in terms of y.

Answer 6

experience/practice