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.
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-> 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.
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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.
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
