Question

Choose the correct words from the drop-down menu to make a true statement about the system of equations.y = 1/3x + 2 –x + 3y = 6Using substitution, the system has choose...A. No solutionB. One solutionC. Infinitely many solutions

Answer 1

C. Infinitely many solutions

Step-by-step explanation:

We were given the system of equations:

`\begin{gathered} y=(1)/(3)x+2--------1 \\ -x+3y=6-------2 \end{gathered}`

We are to proceed using the substitution method, we have:

`\begin{gathered} y=(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((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}`

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