Question

Select the correct choice below and fill in the blank

Answer 1

Hello!

First, let's try to solve the following system:

`\begin{cases}5x+6y=1\text{ equation A} \\ 10x+12y=2\text{ equation B}\end{cases}`

Let's solve it:

• In equation A, we will ,isolate the variable x,:

`\begin{gathered} 5x+6y=1 \\ 5x=1-6y \\ \\ x=(1-6y)/(5) \end{gathered}`

• Now, let's ,replace where's x ,in equation B ,by the value above,:

`\begin{gathered} 10x+12y=2 \\ 10\cdot((1-6y)/(5))+12y=2 \\ \\ (10)/(5)-(60y)/(5)+12y=2 \\ \\ 2\cancel{-12y+12y}=2 \\ 2=2 \end{gathered}`

Notice that the variable y disappeared. So, we can say that this is a system with infinitely many solutions.

The solution set is:

`\mleft\lbrace(1-6y)/(5),y\mright\rbrace`

Answer B.