SOLUTION: Please assist me in solving this system by the substitution method as well as determining whether the equations are independent, dependent, or inconsistent. Thank you. x +

Question 335237: Please assist me in solving this system by the substitution method as well as determining whether the equations are independent, dependent, or inconsistent.
Thank you.

x + 3y = 2
-x +y = 1
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Solve either of the equations for either of the variables in terms of the other. I choose to solve equation 1 for

Use the RHS expression that is equal to

as a substitution into the 2nd equation:

Solve this equation for

. If this substitution produces a value for

you can substitute back into either of the original equations to solve for

. If this substitution produces a trivial identity, such as 0 = 0, then you have infinite solutions. If this substitution produces an absurdity, such as 3 = 0, then you have no solutions.

Consistent systems have at least one solution.

Inconsistent systems have no solutions.

Independent systems have exactly one solution.

Dependent systems have infinite solutions.

A system that represents a pair of lines that intersect in one point is consistent and independent. A system that represents a pair of lines that graph to the same line is consistent and dependent. A system that represents a pair of parallel lines is inconsistent.

John

My calculator said it, I believe it, that settles it

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