Answer: The correct option is (D) (5, -2).
Step-by-step explanation: We are given to use the method of substitution to solve the following system of equations :
![3x+7y=1~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)](https://tex.z-dn.net/?f=3x%2B7y%3D1~~~~~~~~~~~~~~~~~~~~~~~~~%28i%29%5C%5C%5C%5Cy%3Dx-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28ii%29)
Substituting the value of y from equation (ii) in equation (i), we get
![3x+7y=1\\\\\Rightarrow 3x+7(x-7)=1\\\\\Rightarrow 3x+7x-49=1\\\\\Rightarrow 10x=50\\\\\Rightarrow x=\dfrac{50}{10}\\\\\Rightarrow x=5,](https://tex.z-dn.net/?f=3x%2B7y%3D1%5C%5C%5C%5C%5CRightarrow%203x%2B7%28x-7%29%3D1%5C%5C%5C%5C%5CRightarrow%203x%2B7x-49%3D1%5C%5C%5C%5C%5CRightarrow%2010x%3D50%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B50%7D%7B10%7D%5C%5C%5C%5C%5CRightarrow%20x%3D5%2C)
and from equation (ii) again, we get
![y=x-7=5-7=-2.](https://tex.z-dn.net/?f=y%3Dx-7%3D5-7%3D-2.)
Thus, the required solution is (x, y) = (5, -2).
Option (D) is CORRECT.