Substitute the value of y of the second equation into the value of y in the first equation.
[tex]3=-x^2+6x-5[/tex]Equate the expression to 0 by adding x² and 5 and subtracting 6x from both sides of the equation.
[tex]\begin{gathered} x^2-6x+5+3=0 \\ x^2-6x+8=0 \end{gathered}[/tex]Factor the left side of the equation.
[tex](x-2)(x-4)=0[/tex]Equate each factor to 0 and then solve for x.
[tex]\begin{gathered} x-2=0 \\ x=2 \\ \\ x-4=0 \\ x=4 \end{gathered}[/tex]Thus, the equations intersect at
[tex](2,3)\text{ and }(4,3)[/tex]
