Question

Solve the system of equations f(x) = x² - 6xg(x) = x - 6

Answer 1

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:

`\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=(7+5)/(2)=6 \\ x_2=(7-5)/(2)=1 \end{gathered}`

Substituting in g(x),

g(6) = 6 - 6 = 0

g(1) = 1 - 6 = -5

The solutions are (6, 0) and (1, -5)