Respuesta :
Answer:
C. Infinitely many solutions
Explanation:
We were given the system of equations:
[tex]\begin{gathered} y=\frac{1}{3}x+2--------1 \\ -x+3y=6-------2 \end{gathered}[/tex]We are to proceed using the substitution method, we have:
[tex]\begin{gathered} y=\frac{1}{3}x+2--------1 \\ -x+3y=6-------2 \\ \text{We will substitute the value of ''y'' from equation 1 into equation 2, we have:} \\ -x+3(\frac{1}{3}x+2)=6 \\ -x+x+6=6 \\ 6=6(TRUE) \\ \text{We cannot obtain a specific value for the variables ''x'' or ''y''} \end{gathered}[/tex]The system of equations is valid for many different values of ''x'' or ''y''' and as such, the system has infinitely many solutions.
Hence, the correct option is C
