Answer: The required solution of the given system is
(x, y) = (3, 1) and (4, 0).
Step-by-step explanation: We are given to solve the following system of equations :
![x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)](https://tex.z-dn.net/?f=x%2By%3D4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28i%29%5C%5C%5C%5Cy%3Dx%5E2-8x%2B16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28ii%29)
From equation (i), we have
![x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)](https://tex.z-dn.net/?f=x%2By%3D4%5C%5C%5C%5C%5CRightarrow%20y%3D4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28iii%29)
Substituting the value of y from equation (iii) in equation (ii), we get
![y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.](https://tex.z-dn.net/?f=y%3Dx%5E2-8x%2B16%5C%5C%5C%5C%5CRightarrow%204-x%3Dx%5E2-8x%2B16%5C%5C%5C%5C%5CRightarrow%20x%5E2-8x%2B16-4%2Bx%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E2-7x%2B12%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E2-4x-3x%2B12%3D0%5C%5C%5C%5C%5CRightarrow%20x%28x-4%29-3%28x-4%29%3D0%5C%5C%5C%5C%5CRightarrow%20%28x-3%29%28x-4%29%3D0%5C%5C%5C%5C%5CRightarrow%20x-3%3D0%2C~~~~~~~x-4%3D0%5C%5C%5C%5C%5CRightarrow%20x%3D3%2C~4.)
When, x = 3, then from (iii), we get
![y=4-3=1.](https://tex.z-dn.net/?f=y%3D4-3%3D1.)
And, when x = 4, then from (iii), we get
![y=4-4=0.](https://tex.z-dn.net/?f=y%3D4-4%3D0.)
Thus, the required solution of the given system is
(x, y) = (3, 1) and (4, 0).