At the solution of the system,
f(x) = g(x)
x² - 6x = x - 6
x² - 6x - x + 6 = 0
x² - 7x + 6 = 0
Using the quadratic formula, we get:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4\cdot1\cdot6}}{2\cdot1} \\ x_{1,2}=\frac{7\pm\sqrt[]{49^{}-24}}{2} \\ x_1=\frac{7+5}{2}=6 \\ x_2=\frac{7-5}{2}=1 \end{gathered}[/tex]Substituting in g(x),
g(6) = 6 - 6 = 0
g(1) = 1 - 6 = -5
The solutions are (6, 0) and (1, -5)
