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Math  /  Algebra

QuestionConsider the following system. {x=6y+23x−18y=6\left\{\begin{array}{l} x=6 y+2 \\ 3 x-18 y=6 \end{array}\right.
When solving this system by the substitution method, 6=66=6 is obtained. What is the solution set? A. The solution set is □\square \}. (Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y)∣x=6y+2}\{(x, y) \mid x=6 y+2\} or {(x,y)∣3x−18y=6}\{(x, y) \mid 3 x-18 y=6\}. C. The solution is ∅\varnothing.

Studdy Solution
Since the simplification resulted in a true statement without any variables, the system is dependent, and there are infinitely many solutions.
The solution set is described by the equation x=6y+2 x = 6y + 2 .
The solution set is {(x,y)∣x=6y+2}\{(x, y) \mid x = 6y + 2\}. Therefore, the correct answer is:
B. There are infinitely many solutions. The solution set is {(x,y)∣x=6y+2}\{(x, y) \mid x=6y+2\}.

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