Question

2. How many solutions does this system of equations have? Explain howyou know. *9x – 3y = -65y = 15x + 10

Answer 1

Given:

`\begin{gathered} 9x-3y=-6 \\ 5y=15x+10 \end{gathered}`

To determine the solutions of the given system of equations, we first solve for x in 9x-3y=-6:

`\begin{gathered} 9x-3y=-6 \\ \text{Simplify and rearrange} \\ 9x=-6+3y \\ x=(3y-6)/(9) \\ \\ x=(y-2)/(3) \end{gathered}`

Next, we substitute x =(y-2)/3 into 5y=15x+10. So,

`\begin{gathered} 5y=15x+10 \\ 5y=15((y-2)/(3))+10 \\ \text{Simplify} \\ 5y=5(y-2)+10 \\ 5y=5y-10+10 \\ 5y=5y \end{gathered}`

Since 5y=5y is redundant information, this is a dependent system. Therefore, the given system of equations have infinitely many solutions.