As given by the question
There are given that the system of the equation:
[tex]\begin{gathered} 7x+y=7\ldots(1) \\ y=x+2\ldots(2) \end{gathered}[/tex]
Now,
Put the value of y from equation (2), into equation (1):
So,
[tex]\begin{gathered} 7x+y=7 \\ 7x+x+2=7 \\ 8x+2=7 \\ 8x=7-2 \\ 8x=5 \\ x=\frac{5}{8} \end{gathered}[/tex]
Now,
Put the value of x into the equation (2):
[tex]\begin{gathered} y=x+2 \\ y=\frac{5}{8}+2 \\ y=\frac{5+16}{8} \\ y=\frac{21}{8} \end{gathered}[/tex]
So, the value of x and y is shown below:
[tex]\begin{gathered} x=\frac{5}{8},\text{ }y=\frac{21}{8} \\ (\frac{5}{8},\text{ }\frac{\text{21}}{8}) \end{gathered}[/tex]
Hence, the correct option is A.
