Question

How do I solve the following system of equations by substitution. I have to show all steps

Answer 1

In order to solve this system by substitution, let's equate both functions, substitute the expressions for f(x) and g(x), and calculate the values of x:

`\begin{gathered} f(x)=g(x)\\ \\ -x^2+2x+3=-2x+3\\ \\ -x^2+2x+2x+3-3=0\\ \\ -x^2+4x=0\\ \\ x^2=4x\\ \\ x=4\text{ or }x=0 \end{gathered}`

Therefore the solutions are x = 0 and x = 4.