Answer:
Given system of equations:
[tex]\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}[/tex]
To solve by substitution, equate the equations and solve for x:
[tex]\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}[/tex]
Therefore, the x-values of the solution are [tex]x = 0[/tex] and [tex]x = 4[/tex].
To find the y-values of the solution, substitute the found values of x into the functions:
[tex]f(0)=-(0)^2+2(0)+3=3[/tex]
[tex]g(0)=-2(0)+3=3[/tex]
[tex]f(4)=-(4)^2+2(4)+3=-5[/tex]
[tex]g(4)=-2(4)+3=-5[/tex]
Therefore, the solutions to the given system of equations are:
[tex](0, 3)[/tex] and [tex](4, -5)[/tex]
