Question

Determine which of the following ordered pairs satisfies the given system of equations.

Answer 1

As given by the question

There are given that the system of the equation:

`\begin{gathered} 7x+y=7\ldots(1) \\ y=x+2\ldots(2) \end{gathered}`

Now,

Put the value of y from equation (2), into equation (1):

So,

`\begin{gathered} 7x+y=7 \\ 7x+x+2=7 \\ 8x+2=7 \\ 8x=7-2 \\ 8x=5 \\ x=(5)/(8) \end{gathered}`

Now,

Put the value of x into the equation (2):

`\begin{gathered} y=x+2 \\ y=(5)/(8)+2 \\ y=(5+16)/(8) \\ y=(21)/(8) \end{gathered}`

So, the value of x and y is shown below:

`\begin{gathered} x=(5)/(8),\text{ }y=(21)/(8) \\ ((5)/(8),\text{ }\frac{\text{21}}{8}) \end{gathered}`

Hence, the correct option is A.